Question

Fie polinomu P(X)=5Xputeria2(Xputeria4-4x puteria2 - X)-1
a) Scrieti polinomu in forma canonica
b)Completati caseta grad P(X)=?
c)Aflati restu inpartiri polinomului P(X) la binomul Q(X)=X-1 fara a efectua inpartirea
d)Aflati radacina polinomului P(X)-Q(X).
e)Determinati X(X)si R(X), Aflati incit P(X)=(Xla puterea2 -1)* C(X)+R(X)

Answer 1

a)
P(x)=5x^2-x^4+4x^2+x-1=-x^4+9x^2+x-1
P(x)=-x^4+9x^2+x-1

b)
gradP(x)=4

c)
P(1)=-1+9+1-1=8
Rest=8

d)
P(x)=(x^2-1)((-x^2+8)+x+7
C(x)=-x^2+8
R(x)=x+7