Consider the polynomial and the divisor

MATHEMATICS · Subjective · CBSE · Mathematics · Polynomials · Polynomials

Problem

Consider the polynomial

F(x)=2x^{5}-7x^{4}+6x^{3}-x+9

and the divisor

G(x)=x^{2}-3x+1

. (a) Perform the division of

F(x)

G(x)

to obtain the quotient

Q(x)

and remainder

R(x)

. (b) Verify that

F(x)=G(x)\,Q(x)+R(x)

by substituting

x=2

in the three polynomials obtained.