231:@0.918848:0.966558:0.943044:0.966558:0.943044:0.950778:0.918848:0.950778:0.000000:0.000000:0.000000
Demostración. de las propiedades de la adición de polinomios:@0.108233:0.097147:0.578377:0.097147:0.578377:0.080201:0.108233:0.080201:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sin pérdida de generalidad, supondremos que los polinomios que :@0.108233:0.114035:0.599896:0.114035:0.599896:0.097538:0.108233:0.097538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
consideraremos tienen el mismo grado  ::@0.108233:0.131386:0.400368:0.131386:0.400368:0.114888:0.108233:0.114888:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.388250:0.131502:0.397613:0.131502:0.397613:0.115033:0.388250:0.115033:0.000000
Pt:@0.258658:0.152059:0.279846:0.152059:0.279846:0.134874:0.258658:0.134874:0.000000:0.000000
a:@0.303568:0.152059:0.312936:0.152059:0.312936:0.134874:0.303568:0.134874:0.000000
a t:@0.337381:0.152059:0.356234:0.152059:0.356234:0.134874:0.337381:0.134874:0.000000:0.000000:0.000000
a t:@0.408320:0.152059:0.429107:0.152059:0.429107:0.134874:0.408320:0.134874:0.000000:0.000000:0.000000
Qt:@0.258654:0.178266:0.283622:0.178266:0.283622:0.161082:0.258654:0.161082:0.000000:0.000000
b:@0.306922:0.178266:0.316591:0.178266:0.316591:0.161082:0.306922:0.161082:0.000000
b t:@0.340473:0.178266:0.359480:0.178266:0.359480:0.161082:0.340473:0.161082:0.000000:0.000000:0.000000
b t:@0.411165:0.178266:0.432092:0.178266:0.432092:0.161082:0.411165:0.161082:0.000000:0.000000:0.000000
Rt:@0.259067:0.204474:0.280255:0.204474:0.280255:0.187289:0.259067:0.187289:0.000000:0.000000
c:@0.303976:0.204474:0.311475:0.204474:0.311475:0.187289:0.303976:0.187289:0.000000
c t:@0.336543:0.204474:0.354140:0.204474:0.354140:0.187289:0.336543:0.187289:0.000000:0.000000:0.000000
c t:@0.406226:0.204474:0.425756:0.204474:0.425756:0.187289:0.406226:0.187289:0.000000:0.000000:0.000000
n:@0.417229:0.154353:0.422878:0.154353:0.422878:0.144418:0.417229:0.144418:0.000000
n:@0.430165:0.143625:0.435813:0.143625:0.435813:0.133690:0.430165:0.133690:0.000000
n:@0.420216:0.180556:0.425865:0.180556:0.425865:0.170621:0.420216:0.170621:0.000000
n:@0.433151:0.169827:0.438800:0.169827:0.438800:0.159892:0.433151:0.159892:0.000000
n:@0.413882:0.206758:0.419530:0.206758:0.419530:0.196823:0.413882:0.196823:0.000000
n:@0.426817:0.196029:0.432466:0.196029:0.432466:0.186095:0.426817:0.186095:0.000000
()=:@0.268185:0.151939:0.300613:0.151939:0.300613:0.134724:0.268185:0.134724:0.000000:0.000000:0.000000
,:@0.438961:0.151939:0.441835:0.151939:0.441835:0.134724:0.438961:0.134724:0.000000
()=:@0.271954:0.178146:0.304382:0.178146:0.304382:0.160931:0.271954:0.160931:0.000000:0.000000:0.000000
,:@0.441946:0.178146:0.444821:0.178146:0.444821:0.160931:0.441946:0.160931:0.000000
()=:@0.268604:0.204353:0.301031:0.204353:0.301031:0.187138:0.268604:0.187138:0.000000:0.000000:0.000000
,:@0.435600:0.204353:0.438475:0.204353:0.438475:0.187138:0.435600:0.187138:0.000000
0:@0.312736:0.154284:0.317861:0.154284:0.317861:0.144331:0.312736:0.144331:0.000000
1:@0.345824:0.154284:0.350949:0.154284:0.350949:0.144331:0.345824:0.144331:0.000000
0:@0.316246:0.180495:0.321371:0.180495:0.321371:0.170542:0.316246:0.170542:0.000000
1:@0.349067:0.180495:0.354192:0.180495:0.354192:0.170542:0.349067:0.170542:0.000000
0:@0.311899:0.206706:0.317025:0.206706:0.317025:0.196754:0.311899:0.196754:0.000000
1:@0.343732:0.206706:0.348857:0.206706:0.348857:0.196754:0.343732:0.196754:0.000000
:@0.372626:0.152059:0.392729:0.152059:0.392729:0.134543:0.372626:0.134543:0.000000
:@0.375863:0.178266:0.395966:0.178266:0.395966:0.160750:0.375863:0.160750:0.000000
:@0.370515:0.204474:0.390618:0.204474:0.390618:0.186957:0.370515:0.186957:0.000000
+:@0.322871:0.152602:0.296999:0.152602:0.296999:0.135614:0.322871:0.135614:0.000000
+:@0.359780:0.152602:0.333908:0.152602:0.333908:0.135614:0.359780:0.135614:0.000000
+:@0.393815:0.152602:0.404851:0.152602:0.404851:0.135614:0.393815:0.135614:0.000000
+:@0.326389:0.178810:0.300778:0.178810:0.300778:0.161821:0.326389:0.161821:0.000000
+:@0.363037:0.178810:0.337426:0.178810:0.337426:0.161821:0.363037:0.161821:0.000000
+:@0.397071:0.178810:0.408108:0.178810:0.408108:0.161821:0.397071:0.161821:0.000000
+:@0.322047:0.205017:0.297441:0.205017:0.297441:0.188028:0.322047:0.188028:0.000000
+:@0.357690:0.205017:0.333084:0.205017:0.333084:0.188028:0.357690:0.188028:0.000000
+:@0.391724:0.205017:0.402760:0.205017:0.402760:0.188028:0.391724:0.188028:0.000000
donde  ,  ,  ,    ,   = 0,1, ..., :@0.108233:0.228259:0.317288:0.228259:0.317288:0.211761:0.108233:0.211761:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b c:@0.159267:0.228374:0.202721:0.228374:0.202721:0.211906:0.159267:0.211906:0.000000:0.000000:0.000000:0.000000:0.000000
i:@0.168128:0.231604:0.170341:0.231604:0.170341:0.222003:0.168128:0.222003:0.000000
i:@0.186427:0.231604:0.188639:0.231604:0.188639:0.222003:0.186427:0.222003:0.000000
i:@0.202490:0.231604:0.204703:0.231604:0.204703:0.222003:0.202490:0.222003:0.000000
:@0.211599:0.228042:0.227647:0.228042:0.227647:0.213395:0.211599:0.213395:0.000000
:@0.231789:0.227290:0.245698:0.227290:0.245698:0.213843:0.231789:0.213843:0.000000
i:@0.252595:0.228374:0.256390:0.228374:0.256390:0.211906:0.252595:0.211906:0.000000
n, t:@0.317288:0.228374:0.339000:0.228374:0.339000:0.211906:0.317288:0.211906:0.000000:0.000000:0.000000:0.000000
    .:@0.339000:0.228259:0.379996:0.228259:0.379996:0.211761:0.339000:0.211761:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.343142:0.228042:0.359190:0.228042:0.359190:0.213395:0.343142:0.213395:0.000000
:@0.363332:0.227290:0.377241:0.227290:0.377241:0.213843:0.363332:0.213843:0.000000
i) :@0.108241:0.252955:0.122863:0.252955:0.122863:0.236240:0.108241:0.236240:0.000000:0.000000:0.000000
 :@0.122863:0.253200:0.126889:0.253200:0.126889:0.236254:0.122863:0.236254:0.000000
Conmutativa:@0.126889:0.253200:0.228454:0.253200:0.228454:0.236254:0.126889:0.236254:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tomando en cuenta que   +   =   +  ,   =0,1, ...,  , para todo      , :@0.108241:0.277217:0.599901:0.277217:0.599901:0.260719:0.108241:0.260719:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.287485:0.277332:0.296462:0.277332:0.296462:0.260864:0.287485:0.260864:0.000000
i:@0.296369:0.280562:0.298582:0.280562:0.298582:0.270961:0.296369:0.270961:0.000000
b:@0.317480:0.277332:0.326746:0.277332:0.326746:0.260864:0.317480:0.260864:0.000000
i:@0.326684:0.280562:0.328897:0.280562:0.328897:0.270961:0.326684:0.270961:0.000000
b:@0.347797:0.277332:0.357063:0.277332:0.357063:0.260864:0.347797:0.260864:0.000000
i:@0.357001:0.280562:0.359214:0.280562:0.359214:0.270961:0.357001:0.270961:0.000000
a i:@0.378113:0.277332:0.402162:0.277332:0.402162:0.260864:0.378113:0.260864:0.000000:0.000000:0.000000
i :@0.386990:0.280562:0.391617:0.280562:0.391617:0.270961:0.386990:0.270961:0.000000:0.000000
n:@0.458629:0.277332:0.467992:0.277332:0.467992:0.260864:0.458629:0.260864:0.000000
t:@0.549233:0.277332:0.554897:0.277332:0.554897:0.260864:0.549233:0.260864:0.000000
:@0.559001:0.277000:0.575049:0.277000:0.575049:0.262353:0.559001:0.262353:0.000000
:@0.579094:0.276248:0.593004:0.276248:0.593004:0.262801:0.579094:0.262801:0.000000
se tiene:@0.108232:0.294567:0.162504:0.294567:0.162504:0.278070:0.108232:0.278070:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
PQ t:@0.149871:0.313802:0.203640:0.313802:0.203640:0.297333:0.149871:0.297333:0.000000:0.000000:0.000000:0.000000
P t:@0.226354:0.313802:0.246718:0.313802:0.246718:0.297333:0.226354:0.297333:0.000000:0.000000:0.000000
Q t:@0.268333:0.313802:0.292318:0.313802:0.292318:0.297333:0.268333:0.297333:0.000000:0.000000:0.000000
a:@0.315456:0.313802:0.324434:0.313802:0.324434:0.297333:0.315456:0.297333:0.000000
b:@0.346762:0.313802:0.356029:0.313802:0.356029:0.297333:0.346762:0.297333:0.000000
a:@0.384194:0.313802:0.393172:0.313802:0.393172:0.297333:0.384194:0.297333:0.000000
bt:@0.413670:0.313802:0.439023:0.313802:0.439023:0.297333:0.413670:0.297333:0.000000:0.000000
a:@0.492870:0.313802:0.501847:0.313802:0.501847:0.297333:0.492870:0.297333:0.000000
b t:@0.524234:0.313802:0.551455:0.313802:0.551455:0.297333:0.524234:0.297333:0.000000:0.000000:0.000000
b:@0.226874:0.335288:0.236141:0.335288:0.236141:0.318819:0.226874:0.318819:0.000000
a:@0.258758:0.335288:0.267736:0.335288:0.267736:0.318819:0.258758:0.318819:0.000000
b:@0.295613:0.335288:0.304879:0.335288:0.304879:0.318819:0.295613:0.318819:0.000000
a t:@0.325667:0.335288:0.350846:0.335288:0.350846:0.318819:0.325667:0.318819:0.000000:0.000000:0.000000
b:@0.404288:0.335288:0.413555:0.335288:0.413555:0.318819:0.404288:0.318819:0.000000
at:@0.436230:0.335288:0.463298:0.335288:0.463298:0.318819:0.436230:0.318819:0.000000:0.000000
Qt:@0.226874:0.355010:0.250860:0.355010:0.250860:0.338541:0.226874:0.338541:0.000000:0.000000
Pt:@0.272475:0.355010:0.292858:0.355010:0.292858:0.338541:0.272475:0.338541:0.000000:0.000000
QP t:@0.321101:0.355010:0.374870:0.355010:0.374870:0.338541:0.321101:0.338541:0.000000:0.000000:0.000000:0.000000
n:@0.501462:0.315972:0.506881:0.315972:0.506881:0.306440:0.501462:0.306440:0.000000
n:@0.532974:0.315972:0.538393:0.315972:0.538393:0.306440:0.532974:0.306440:0.000000
n:@0.552505:0.305717:0.557924:0.305717:0.557924:0.296185:0.552505:0.296185:0.000000
n:@0.413043:0.337460:0.418462:0.337460:0.418462:0.327928:0.413043:0.327928:0.000000
n:@0.444822:0.337460:0.450242:0.337460:0.450242:0.327928:0.444822:0.327928:0.000000
n:@0.464347:0.327208:0.469767:0.327208:0.469767:0.317676:0.464347:0.317676:0.000000
(:@0.144323:0.313686:0.150276:0.313686:0.150276:0.297188:0.144323:0.297188:0.000000
)() =( ):@0.186841:0.313686:0.252921:0.313686:0.252921:0.297188:0.186841:0.297188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( )=:@0.281106:0.313686:0.312374:0.313686:0.312374:0.297188:0.281106:0.297188:0.000000:0.000000:0.000000:0.000000
(:@0.378222:0.313686:0.384175:0.313686:0.384175:0.297188:0.378222:0.297188:0.000000
):@0.427426:0.313686:0.433379:0.313686:0.433379:0.297188:0.427426:0.297188:0.000000
(:@0.486909:0.313686:0.492862:0.313686:0.492862:0.297188:0.486909:0.297188:0.000000
):@0.539889:0.313686:0.545842:0.313686:0.545842:0.297188:0.539889:0.297188:0.000000
=:@0.213426:0.335178:0.224234:0.335178:0.224234:0.318681:0.213426:0.318681:0.000000
(:@0.290064:0.335178:0.296017:0.335178:0.296017:0.318681:0.290064:0.318681:0.000000
):@0.339286:0.335178:0.345239:0.335178:0.345239:0.318681:0.339286:0.318681:0.000000
(:@0.398758:0.335178:0.404711:0.335178:0.404711:0.318681:0.398758:0.318681:0.000000
):@0.451738:0.335178:0.457691:0.335178:0.457691:0.318681:0.451738:0.318681:0.000000
=( ):@0.213426:0.354900:0.257081:0.354900:0.257081:0.338403:0.213426:0.338403:0.000000:0.000000:0.000000:0.000000
( )=(:@0.281645:0.354900:0.321524:0.354900:0.321524:0.338403:0.281645:0.338403:0.000000:0.000000:0.000000:0.000000:0.000000
)().:@0.358089:0.354900:0.384232:0.354900:0.384232:0.338403:0.358089:0.338403:0.000000:0.000000:0.000000:0.000000
0:@0.324254:0.315905:0.329171:0.315905:0.329171:0.306356:0.324254:0.306356:0.000000
0:@0.355721:0.315905:0.360638:0.315905:0.360638:0.306356:0.355721:0.306356:0.000000
1:@0.392306:0.315905:0.397224:0.315905:0.397224:0.306356:0.392306:0.306356:0.000000
1:@0.421934:0.315905:0.426851:0.315905:0.426851:0.306356:0.421934:0.306356:0.000000
0:@0.235828:0.337396:0.240746:0.337396:0.240746:0.327847:0.235828:0.327847:0.000000
0:@0.267552:0.337396:0.272470:0.337396:0.272470:0.327847:0.267552:0.327847:0.000000
1:@0.303881:0.337396:0.308799:0.337396:0.308799:0.327847:0.303881:0.327847:0.000000
1:@0.333776:0.337396:0.338694:0.337396:0.338694:0.327847:0.333776:0.327847:0.000000
+:@0.161388:0.314322:0.078105:0.314322:0.078105:0.298041:0.161388:0.298041:0.000000
+:@0.255249:0.314322:0.171965:0.314322:0.171965:0.298041:0.255249:0.298041:0.000000
+:@0.333678:0.314322:0.312794:0.314322:0.312794:0.298041:0.333678:0.298041:0.000000
+:@0.365138:0.314322:0.344254:0.314322:0.344254:0.298041:0.365138:0.298041:0.000000
+:@0.400586:0.314322:0.369704:0.314322:0.369704:0.298041:0.400586:0.298041:0.000000
+:@0.442045:0.314322:0.411162:0.314322:0.411162:0.298041:0.442045:0.298041:0.000000
+:@0.473832:0.314322:0.447073:0.314322:0.447073:0.298041:0.473832:0.298041:0.000000
+:@0.511168:0.314322:0.484409:0.314322:0.484409:0.298041:0.511168:0.298041:0.000000
+:@0.245269:0.335808:0.224116:0.335808:0.224116:0.319527:0.245269:0.319527:0.000000
+:@0.276999:0.335808:0.255846:0.335808:0.255846:0.319527:0.276999:0.319527:0.000000
+:@0.312178:0.335808:0.281026:0.335808:0.281026:0.319527:0.312178:0.319527:0.000000
+:@0.353906:0.335808:0.322754:0.335808:0.322754:0.319527:0.353906:0.319527:0.000000
+:@0.385675:0.335808:0.359185:0.335808:0.359185:0.319527:0.385675:0.319527:0.000000
+:@0.422741:0.335808:0.396251:0.335808:0.396251:0.319527:0.422741:0.319527:0.000000
+:@0.259390:0.355539:0.193117:0.355539:0.193117:0.339258:0.259390:0.339258:0.000000
+:@0.336239:0.355539:0.269967:0.355539:0.269967:0.339258:0.336239:0.339258:0.000000
 :@0.562241:0.360324:0.566383:0.360324:0.566383:0.343827:0.562241:0.343827:0.000000
Conclusión :@0.108236:0.378138:0.201500:0.378138:0.201500:0.361192:0.108236:0.361192:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
::@0.194718:0.377675:0.197473:0.377675:0.197473:0.361177:0.194718:0.361177:0.000000
P + Q = Q + P.:@0.201500:0.377791:0.301486:0.377791:0.301486:0.361322:0.201500:0.361322:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ii):@0.108236:0.402862:0.125575:0.402862:0.125575:0.385671:0.108236:0.385671:0.000000:0.000000:0.000000
 :@0.125575:0.402371:0.129659:0.402371:0.129659:0.385656:0.125575:0.385656:0.000000
 :@0.129659:0.402617:0.133686:0.402617:0.133686:0.385671:0.129659:0.385671:0.000000
Existencia de elemento neutro:@0.133686:0.402617:0.365655:0.402617:0.365655:0.385671:0.133686:0.385671:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tenemos que   + 0 =   = :@0.108236:0.426633:0.305487:0.426633:0.305487:0.410135:0.108236:0.410135:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.210889:0.426749:0.219867:0.426749:0.219867:0.410280:0.210889:0.410280:0.000000
i:@0.219737:0.429977:0.221950:0.429977:0.221950:0.420376:0.219737:0.420376:0.000000
a:@0.273993:0.426749:0.282971:0.426749:0.282971:0.410280:0.273993:0.410280:0.000000
i:@0.282843:0.429977:0.285056:0.429977:0.285056:0.420376:0.282843:0.420376:0.000000
0 + a i:@0.306826:0.426749:0.359837:0.426749:0.359837:0.410280:0.306826:0.410280:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i:@0.345603:0.429977:0.347815:0.429977:0.347815:0.420376:0.345603:0.420376:0.000000
,   =0,1, ...,  ,  y de la definición del :@0.347816:0.426633:0.599894:0.426633:0.599894:0.410135:0.347816:0.410135:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.420600:0.426749:0.429963:0.426749:0.429963:0.410280:0.420600:0.410280:0.000000
polinomio nulo, se sigue que para todo      ,:@0.108214:0.443984:0.437611:0.443984:0.437611:0.427486:0.108214:0.427486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.390947:0.444099:0.396611:0.444099:0.396611:0.427631:0.390947:0.427631:0.000000
:@0.400753:0.443767:0.416801:0.443767:0.416801:0.429120:0.400753:0.429120:0.000000
:@0.420947:0.443015:0.434856:0.443015:0.434856:0.429568:0.420947:0.429568:0.000000
P:@0.202170:0.466967:0.210489:0.466967:0.210489:0.450498:0.202170:0.450498:0.000000
t:@0.244404:0.466967:0.249767:0.466967:0.249767:0.450498:0.244404:0.450498:0.000000
Pt:@0.271276:0.466967:0.290578:0.466967:0.290578:0.450498:0.271276:0.450498:0.000000:0.000000
t:@0.324675:0.466967:0.330038:0.466967:0.330038:0.450498:0.324675:0.450498:0.000000
a:@0.272772:0.487513:0.281274:0.487513:0.281274:0.471045:0.272772:0.471045:0.000000
a:@0.331370:0.487513:0.339871:0.487513:0.339871:0.471045:0.331370:0.471045:0.000000
t:@0.373257:0.487513:0.378620:0.487513:0.378620:0.471045:0.373257:0.471045:0.000000
a:@0.429629:0.487513:0.438130:0.487513:0.438130:0.471045:0.429629:0.471045:0.000000
t:@0.473303:0.487513:0.478667:0.487513:0.478667:0.471045:0.473303:0.471045:0.000000
a:@0.272772:0.508999:0.281274:0.508999:0.281274:0.492531:0.272772:0.492531:0.000000
a t:@0.302819:0.508999:0.320023:0.508999:0.320023:0.492531:0.302819:0.492531:0.000000:0.000000:0.000000
a t:@0.365777:0.508999:0.384768:0.508999:0.384768:0.492531:0.365777:0.492531:0.000000:0.000000:0.000000
Pt:@0.272371:0.528721:0.291672:0.528721:0.291672:0.512253:0.272371:0.512253:0.000000:0.000000
n:@0.437748:0.489686:0.442880:0.489686:0.442880:0.480153:0.437748:0.480153:0.000000
n:@0.479637:0.479434:0.484768:0.479434:0.484768:0.469902:0.479637:0.469902:0.000000
n:@0.373895:0.511177:0.379027:0.511177:0.379027:0.501645:0.373895:0.501645:0.000000
n:@0.385743:0.500925:0.390875:0.500925:0.390875:0.491393:0.385743:0.491393:0.000000
+:@0.213076:0.467488:0.137530:0.467488:0.137530:0.451207:0.213076:0.451207:0.000000
+:@0.298638:0.467488:0.223092:0.467488:0.223092:0.451207:0.298638:0.451207:0.000000
++:@0.290008:0.488034:0.323321:0.488034:0.323321:0.471753:0.290008:0.471753:0.000000:0.000000
+:@0.346873:0.488034:0.322281:0.488034:0.322281:0.471753:0.346873:0.471753:0.000000
+:@0.381481:0.488034:0.356889:0.488034:0.356889:0.471753:0.381481:0.471753:0.000000
+:@0.411564:0.488034:0.386224:0.488034:0.386224:0.471753:0.411564:0.471753:0.000000
+:@0.446920:0.488034:0.421580:0.488034:0.421580:0.471753:0.446920:0.471753:0.000000
+:@0.290008:0.509520:0.267150:0.509520:0.267150:0.493239:0.290008:0.493239:0.000000
+:@0.322883:0.509520:0.300024:0.509520:0.300024:0.493239:0.322883:0.493239:0.000000
+:@0.352966:0.509520:0.362982:0.509520:0.362982:0.493239:0.352966:0.493239:0.000000
(:@0.196913:0.466837:0.202550:0.466837:0.202550:0.450339:0.196913:0.450339:0.000000
0)( )= () 0( ):@0.225865:0.466837:0.335909:0.466837:0.335909:0.450339:0.225865:0.450339:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.259633:0.487383:0.269868:0.487383:0.269868:0.470886:0.259633:0.470886:0.000000
0 (:@0.302815:0.487383:0.331348:0.487383:0.331348:0.470886:0.302815:0.470886:0.000000:0.000000:0.000000
0):@0.359662:0.487383:0.373289:0.487383:0.373289:0.470886:0.359662:0.470886:0.000000:0.000000
(:@0.423969:0.487383:0.429607:0.487383:0.429607:0.470886:0.423969:0.470886:0.000000
0):@0.459708:0.487383:0.473318:0.487383:0.473318:0.470886:0.459708:0.470886:0.000000:0.000000
=:@0.259633:0.508869:0.269868:0.508869:0.269868:0.492372:0.259633:0.492372:0.000000
=( ).:@0.259633:0.528591:0.299824:0.528591:0.299824:0.512094:0.259633:0.512094:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.281093:0.489619:0.285749:0.489619:0.285749:0.480070:0.281093:0.480070:0.000000
1:@0.339043:0.489619:0.343699:0.489619:0.343699:0.480070:0.339043:0.480070:0.000000
0:@0.281093:0.511110:0.285749:0.511110:0.285749:0.501561:0.281093:0.501561:0.000000
1:@0.310490:0.511110:0.315147:0.511110:0.315147:0.501561:0.310490:0.501561:0.000000
De manera similar, se muestra que (0 +  )( ) =  ( ) para todo      .:@0.108233:0.551821:0.591787:0.551821:0.591787:0.535324:0.108233:0.535324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P t:@0.388599:0.551937:0.414954:0.551937:0.414954:0.535468:0.388599:0.535468:0.000000:0.000000:0.000000
P t:@0.439998:0.551937:0.460400:0.551937:0.460400:0.535468:0.439998:0.535468:0.000000:0.000000:0.000000
t:@0.545127:0.551937:0.550791:0.551937:0.550791:0.535468:0.545127:0.535468:0.000000
:@0.554933:0.551604:0.570981:0.551604:0.570981:0.536957:0.554933:0.536957:0.000000
:@0.575122:0.550852:0.589032:0.550852:0.589032:0.537406:0.575122:0.537406:0.000000
Conclusión :@0.108229:0.569635:0.201496:0.569635:0.201496:0.552689:0.108229:0.552689:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:  + 0 = 0 +   =  .:@0.194714:0.569172:0.323965:0.569172:0.323965:0.552674:0.194714:0.552674:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.201496:0.569288:0.210281:0.569288:0.210281:0.552819:0.201496:0.552819:0.000000
P P:@0.284548:0.569288:0.321210:0.569288:0.321210:0.552819:0.284548:0.552819:0.000000:0.000000:0.000000
La Demostración. del resto de propiedades del teorema se deja como :@0.108233:0.586523:0.599840:0.586523:0.599840:0.570025:0.108233:0.570025:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tarea para el estudiante.:@0.108233:0.603873:0.276185:0.603873:0.276185:0.587376:0.108233:0.587376:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Resta:@0.108233:0.635195:0.151716:0.635195:0.151716:0.617512:0.108233:0.617512:0.000000:0.000000:0.000000:0.000000:0.000000
Sea   un polinomio con coeficientes reales. Existe el opuesto aditivo :@0.108233:0.651902:0.599902:0.651902:0.599902:0.635405:0.108233:0.635405:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q:@0.136803:0.652018:0.148690:0.652018:0.148690:0.635549:0.136803:0.635549:0.000000
– de   tal que  + (:@0.108233:0.669253:0.266247:0.669253:0.266247:0.652755:0.108233:0.652755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q :@0.118733:0.669369:0.134761:0.669369:0.134761:0.652900:0.118733:0.652900:0.000000:0.000000
Q:@0.157687:0.669369:0.169574:0.669369:0.169574:0.652900:0.157687:0.652900:0.000000
Q :@0.228390:0.669369:0.244419:0.669369:0.244419:0.652900:0.228390:0.652900:0.000000:0.000000
–Q:@0.266247:0.669369:0.288171:0.669369:0.288171:0.652900:0.266247:0.652900:0.000000:0.000000
) = 0. Si  un polinomio, podemos sumar   :@0.288171:0.669253:0.599900:0.669253:0.599900:0.652755:0.288171:0.652755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P :@0.346409:0.669369:0.359336:0.669369:0.359336:0.652900:0.346409:0.652900:0.000000:0.000000
P:@0.586973:0.669369:0.595758:0.669369:0.595758:0.652900:0.586973:0.652900:0.000000
con el opuesto aditivo de   que nos da el polinomio  + (– ). Este :@0.108233:0.686604:0.599902:0.686604:0.599902:0.670106:0.108233:0.670106:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q:@0.296917:0.686720:0.308804:0.686720:0.308804:0.670251:0.296917:0.670251:0.000000
P :@0.495251:0.686720:0.508178:0.686720:0.508178:0.670251:0.495251:0.670251:0.000000:0.000000
Q:@0.541355:0.686720:0.553241:0.686720:0.553241:0.670251:0.541355:0.670251:0.000000
hecho nos conduce a definir otra operación en polinomios con coe-:@0.108233:0.703955:0.595735:0.703955:0.595735:0.687457:0.108233:0.687457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ficiente real que es la resta.:@0.108233:0.721305:0.296222:0.721305:0.296222:0.704808:0.108233:0.704808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.108233:0.739119:0.188317:0.739119:0.188317:0.722173:0.108233:0.722173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Para todo :@0.188319:0.738656:0.268693:0.738656:0.268693:0.722158:0.188319:0.722158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P, Q:@0.268559:0.738772:0.294374:0.738772:0.294374:0.722303:0.268559:0.722303:0.000000:0.000000:0.000000:0.000000
 polinomios con coeficiente real, el polino-:@0.294393:0.738656:0.595715:0.738656:0.595715:0.722158:0.294393:0.722158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mio notado  –   se define como: ( –  ) ( ) = ( ) – ( ),  :@0.108233:0.756007:0.535147:0.756007:0.535147:0.739509:0.108233:0.739509:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P  Q:@0.197526:0.756123:0.236981:0.756123:0.236981:0.739654:0.197526:0.739654:0.000000:0.000000:0.000000:0.000000
P  Q t:@0.363301:0.756123:0.424468:0.756123:0.424468:0.739654:0.363301:0.739654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 P t:@0.445371:0.756123:0.469915:0.756123:0.469915:0.739654:0.445371:0.739654:0.000000:0.000000:0.000000:0.000000
 Q t:@0.490510:0.756123:0.518155:0.756123:0.518155:0.739654:0.490510:0.739654:0.000000:0.000000:0.000000:0.000000
t:@0.545814:0.756123:0.551478:0.756123:0.551478:0.739654:0.545814:0.739654:0.000000
:@0.551478:0.755790:0.567526:0.755790:0.567526:0.741143:0.551478:0.741143:0.000000
:@0.567525:0.755038:0.581435:0.755038:0.581435:0.741591:0.567525:0.741591:0.000000
.:@0.581435:0.756007:0.584190:0.756007:0.584190:0.739509:0.581435:0.739509:0.000000
Ejercicio resuelto:@0.108241:0.782539:0.226220:0.782539:0.226220:0.765752:0.108241:0.765752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. :@0.108241:0.799731:0.124598:0.799731:0.124598:0.783016:0.108241:0.783016:0.000000:0.000000:0.000000
  Sean :@0.124598:0.799513:0.169775:0.799513:0.169775:0.783016:0.124598:0.783016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P, Q:@0.169775:0.799629:0.195725:0.799629:0.195725:0.783160:0.169775:0.783160:0.000000:0.000000:0.000000:0.000000
 los polinomios definidos por::@0.195725:0.799513:0.407521:0.799513:0.407521:0.783016:0.195725:0.783016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,       :@0.309717:0.839695:0.341467:0.839695:0.341467:0.823197:0.309717:0.823197:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.352131:0.839805:0.357795:0.839805:0.357795:0.823336:0.352131:0.823336:0.000000
:@0.357795:0.839472:0.373843:0.839472:0.373843:0.824825:0.357795:0.824825:0.000000
:@0.373842:0.838720:0.387752:0.838720:0.387752:0.825274:0.373842:0.825274:0.000000
.:@0.387752:0.839689:0.390507:0.839689:0.390507:0.823191:0.387752:0.823191:0.000000
Pt:@0.172205:0.823547:0.192588:0.823547:0.192588:0.807078:0.172205:0.807078:0.000000:0.000000
t:@0.247802:0.823547:0.253466:0.823547:0.253466:0.807078:0.247802:0.807078:0.000000
t:@0.277490:0.823547:0.283154:0.823547:0.283154:0.807078:0.277490:0.807078:0.000000
t:@0.315443:0.823547:0.321107:0.823547:0.321107:0.807078:0.315443:0.807078:0.000000
Qt:@0.172205:0.839775:0.196191:0.839775:0.196191:0.823306:0.172205:0.823306:0.000000:0.000000
t:@0.263080:0.839775:0.268744:0.839775:0.268744:0.823306:0.263080:0.823306:0.000000
t:@0.294020:0.839775:0.299684:0.839775:0.299684:0.823306:0.294020:0.823306:0.000000
() =3 8:@0.181367:0.823431:0.247543:0.823431:0.247543:0.806933:0.181367:0.806933:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.269159:0.823431:0.277655:0.823431:0.277655:0.806933:0.269159:0.806933:0.000000
2,:@0.306688:0.823431:0.332889:0.823431:0.332889:0.806933:0.306688:0.806933:0.000000:0.000000
() =7 4:@0.184979:0.839659:0.262830:0.839659:0.262830:0.823161:0.184979:0.823161:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
9:@0.285274:0.839659:0.293770:0.839659:0.293770:0.823161:0.285274:0.823161:0.000000
2:@0.284185:0.815395:0.289103:0.815395:0.289103:0.805846:0.284185:0.805846:0.000000
3:@0.322142:0.815395:0.327060:0.815395:0.327060:0.805846:0.322142:0.805846:0.000000
2:@0.300728:0.831622:0.305646:0.831622:0.305646:0.822073:0.300728:0.822073:0.000000
{:@0.163095:0.844847:0.172343:0.844847:0.172343:0.799587:0.163095:0.799587:0.000000
−:@0.225971:0.824067:0.236547:0.824067:0.236547:0.807786:0.225971:0.807786:0.000000
+:@0.256487:0.824067:0.267063:0.824067:0.267063:0.807786:0.256487:0.807786:0.000000
−:@0.293611:0.824067:0.304188:0.824067:0.304188:0.807786:0.293611:0.807786:0.000000
−+:@0.219322:0.840295:0.251417:0.840295:0.251417:0.824014:0.219322:0.824014:0.000000:0.000000
−:@0.271781:0.840295:0.282357:0.840295:0.282357:0.824014:0.271781:0.824014:0.000000
El opuesto aditivo de   es el polinomio –  dado por :@0.108233:0.867159:0.498501:0.867159:0.498501:0.850661:0.108233:0.850661:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q:@0.266050:0.867274:0.277937:0.867274:0.277937:0.850806:0.266050:0.850806:0.000000
Q:@0.409902:0.867274:0.421789:0.867274:0.421789:0.850806:0.409902:0.850806:0.000000
– ( ) = 7 – 4  + 9 .:@0.108233:0.884509:0.249678:0.884509:0.249678:0.868012:0.108233:0.868012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q t:@0.118733:0.884625:0.142236:0.884625:0.142236:0.868156:0.118733:0.868156:0.000000:0.000000:0.000000
t:@0.203057:0.884625:0.208721:0.884625:0.208721:0.868156:0.203057:0.868156:0.000000
t:@0.236308:0.884625:0.241972:0.884625:0.241972:0.868156:0.236308:0.868156:0.000000
2:@0.241971:0.878158:0.246924:0.878158:0.246924:0.868540:0.241971:0.868540:0.000000
Entonces,  –   es el polinomio :@0.108232:0.901860:0.337215:0.901860:0.337215:0.885362:0.108232:0.885362:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P  Q:@0.180379:0.901976:0.219834:0.901976:0.219834:0.885507:0.180379:0.885507:0.000000:0.000000:0.000000:0.000000
PQ t:@0.138615:0.921986:0.191778:0.921986:0.191778:0.905703:0.138615:0.905703:0.000000:0.000000:0.000000:0.000000
P t:@0.214236:0.921986:0.234369:0.921986:0.234369:0.905703:0.214236:0.905703:0.000000:0.000000:0.000000
Q t:@0.272656:0.921986:0.296371:0.921986:0.296371:0.905703:0.272656:0.905703:0.000000:0.000000:0.000000
P t:@0.324371:0.921986:0.344505:0.921986:0.344505:0.905703:0.324371:0.905703:0.000000:0.000000:0.000000
Q t:@0.365877:0.921986:0.389591:0.921986:0.389591:0.905703:0.365877:0.905703:0.000000:0.000000:0.000000
t:@0.178559:0.938026:0.184159:0.938026:0.184159:0.921743:0.178559:0.921743:0.000000
t:@0.207912:0.938026:0.213512:0.938026:0.213512:0.921743:0.207912:0.921743:0.000000
t:@0.245436:0.938026:0.251036:0.938026:0.251036:0.921743:0.245436:0.921743:0.000000
t:@0.307075:0.938026:0.312676:0.938026:0.312676:0.921743:0.307075:0.921743:0.000000
t:@0.337667:0.938026:0.343267:0.938026:0.343267:0.921743:0.337667:0.921743:0.000000
t:@0.415306:0.938026:0.420906:0.938026:0.420906:0.921743:0.415306:0.921743:0.000000
t:@0.453040:0.938026:0.458640:0.938026:0.458640:0.921743:0.453040:0.921743:0.000000
t:@0.490565:0.938026:0.496165:0.938026:0.496165:0.921743:0.490565:0.921743:0.000000
(:@0.133110:0.921871:0.138996:0.921871:0.138996:0.905560:0.133110:0.905560:0.000000
)() =( )(:@0.175149:0.921871:0.261608:0.921871:0.261608:0.905560:0.175149:0.905560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
())= ():@0.285266:0.921871:0.350619:0.921871:0.350619:0.905560:0.285266:0.905560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
():@0.378486:0.921871:0.395706:0.921871:0.395706:0.905560:0.378486:0.905560:0.000000:0.000000
=3 8:@0.133091:0.937911:0.178292:0.937911:0.178292:0.921600:0.133091:0.921600:0.000000:0.000000:0.000000:0.000000
5:@0.199664:0.937911:0.208064:0.937911:0.208064:0.921600:0.199664:0.921600:0.000000
2:@0.236770:0.937911:0.245170:0.937911:0.245170:0.921600:0.236770:0.921600:0.000000
7 4:@0.274084:0.937911:0.306809:0.937911:0.306809:0.921600:0.274084:0.921600:0.000000:0.000000:0.000000
9 =1012:@0.329000:0.937911:0.415039:0.937911:0.415039:0.921600:0.329000:0.921600:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
14:@0.436049:0.937911:0.452774:0.937911:0.452774:0.921600:0.436049:0.921600:0.000000:0.000000
2 ,:@0.481898:0.937911:0.507822:0.937911:0.507822:0.921600:0.481898:0.921600:0.000000:0.000000:0.000000
t:@0.527308:0.937911:0.533480:0.937911:0.533480:0.921600:0.527308:0.921600:0.000000
.:@0.565347:0.937911:0.568071:0.937911:0.568071:0.921600:0.565347:0.921600:0.000000
2:@0.214547:0.929970:0.219409:0.929970:0.219409:0.920529:0.214547:0.920529:0.000000
3:@0.252077:0.929970:0.256939:0.929970:0.256939:0.920529:0.252077:0.920529:0.000000
2:@0.344311:0.929970:0.349173:0.929970:0.349173:0.920529:0.344311:0.920529:0.000000
2:@0.459689:0.929970:0.464551:0.929970:0.464551:0.920529:0.459689:0.920529:0.000000
3:@0.497214:0.929970:0.502076:0.929970:0.502076:0.920529:0.497214:0.920529:0.000000
−:@0.150002:0.922500:0.160459:0.922500:0.160459:0.906403:0.150002:0.906403:0.000000
+ −:@0.242804:0.922500:0.272099:0.922500:0.272099:0.906403:0.242804:0.906403:0.000000:0.000000:0.000000
−:@0.352958:0.922500:0.363415:0.922500:0.363415:0.906403:0.352958:0.906403:0.000000
−:@0.156973:0.938540:0.167431:0.938540:0.167431:0.922443:0.156973:0.922443:0.000000
+:@0.187145:0.938540:0.197603:0.938540:0.197603:0.922443:0.187145:0.922443:0.000000
−:@0.223851:0.938540:0.234308:0.938540:0.234308:0.922443:0.223851:0.922443:0.000000
+ −:@0.261166:0.938540:0.295547:0.938540:0.295547:0.922443:0.261166:0.922443:0.000000:0.000000:0.000000
+:@0.315681:0.938540:0.326139:0.938540:0.326139:0.922443:0.315681:0.922443:0.000000
−:@0.386178:0.938540:0.396635:0.938540:0.396635:0.922443:0.386178:0.922443:0.000000
+:@0.423912:0.938540:0.434369:0.938540:0.434369:0.922443:0.423912:0.922443:0.000000
−:@0.468998:0.938540:0.479456:0.938540:0.479456:0.922443:0.468998:0.922443:0.000000
∀ ∈:@0.513875:0.938540:0.550638:0.938540:0.550638:0.922443:0.513875:0.922443:0.000000:0.000000:0.000000
Interdisciplinariedad:@0.684403:0.293018:0.831188:0.293018:0.831188:0.277546:0.684403:0.277546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática  :@0.684639:0.322070:0.776653:0.322070:0.776653:0.306597:0.684639:0.306597:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y Economía:@0.638096:0.337912:0.719114:0.337912:0.719114:0.322439:0.638096:0.322439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los polinomios se pueden :@0.638096:0.353331:0.812287:0.353331:0.812287:0.338268:0.638096:0.338268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
utilizar para modelar situacio-:@0.638096:0.369173:0.830705:0.369173:0.830705:0.354110:0.638096:0.354110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nes de mercado, por ejemplo: :@0.638096:0.385015:0.834083:0.385015:0.834083:0.369952:0.638096:0.369952:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para el análisis de la variación de :@0.638096:0.400857:0.849878:0.400857:0.849878:0.385794:0.638096:0.385794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los precios de un producto en :@0.638096:0.416699:0.836966:0.416699:0.836966:0.401636:0.638096:0.401636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función del tiempo. :@0.638096:0.432541:0.769263:0.432541:0.769263:0.417478:0.638096:0.417478:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las personas del ámbito del :@0.638103:0.599624:0.821651:0.599624:0.821651:0.584561:0.638103:0.584561:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
negocio suelen utilizar estas  :@0.638103:0.615466:0.825627:0.615466:0.825627:0.600403:0.638103:0.600403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
expresiones para determinar ac-:@0.638103:0.631308:0.843783:0.631308:0.843783:0.616245:0.638103:0.616245:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ciones que afectan a sus ventas. :@0.638103:0.647150:0.846752:0.647150:0.846752:0.632087:0.638103:0.632087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Shutterstock, 526494319:@0.866555:0.583239:0.866555:0.515066:0.855087:0.515066:0.855087:0.583239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.684403:0.100106:0.782026:0.100106:0.782026:0.084633:0.684403:0.084633:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.684403:0.112674:0.768466:0.112674:0.768466:0.097201:0.684403:0.097201:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Debido a la propiedad :@0.684639:0.137148:0.833535:0.137148:0.833535:0.122085:0.684639:0.122085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
asociativa y conmutativa, a la :@0.638096:0.152990:0.831110:0.152990:0.831110:0.137927:0.638096:0.137927:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
suma de los polinomios :@0.638096:0.170337:0.796510:0.170337:0.796510:0.155274:0.638096:0.155274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P, :@0.796510:0.170443:0.809351:0.170443:0.809351:0.155406:0.796510:0.155406:0.000000:0.000000:0.000000
Q, R:@0.809356:0.170777:0.837368:0.170777:0.837368:0.154309:0.809356:0.154309:0.000000:0.000000:0.000000:0.000000
 :@0.837368:0.170341:0.841150:0.170341:0.841150:0.155278:0.837368:0.155278:0.000000
la escribiremos :@0.638108:0.187688:0.738070:0.187688:0.738070:0.172625:0.638108:0.172625:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P + :@0.738070:0.187794:0.763594:0.187794:0.763594:0.172757:0.738070:0.172757:0.000000:0.000000:0.000000:0.000000
Q + R:@0.763587:0.188128:0.804217:0.188128:0.804217:0.171659:0.763587:0.171659:0.000000:0.000000:0.000000:0.000000:0.000000
,  :@0.804216:0.187692:0.814295:0.187692:0.814295:0.172629:0.804216:0.172629:0.000000:0.000000:0.000000
en vez de :@0.638096:0.205039:0.703002:0.205039:0.703002:0.189976:0.638096:0.189976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P + (:@0.703002:0.205144:0.733485:0.205144:0.733485:0.190108:0.703002:0.190108:0.000000:0.000000:0.000000:0.000000:0.000000
Q + R):@0.733491:0.205479:0.779554:0.205479:0.779554:0.189010:0.733491:0.189010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 o en vez :@0.779554:0.205043:0.840644:0.205043:0.840644:0.189979:0.779554:0.189979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de (:@0.638095:0.222390:0.663618:0.222390:0.663618:0.207326:0.638095:0.207326:0.000000:0.000000:0.000000:0.000000
P + :@0.663618:0.222495:0.689141:0.222495:0.689141:0.207458:0.663618:0.207458:0.000000:0.000000:0.000000:0.000000
Q) + R.:@0.689148:0.222830:0.738158:0.222830:0.738158:0.206361:0.689148:0.206361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Recuerda los elementos de un polinomio.:@0.640969:0.899930:0.848911:0.899930:0.848911:0.888453:0.640969:0.888453:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000