Let be a polynomial in and let .

MATHEMATICS · Multi-part · CBSE · Mathematics · Polynomials · Polynomials

Problem

Let

p(x)=2x^{4}-3x^{3}+5x^{2}-9x+k

be a polynomial in

x

and let

d(x)=x^{2}-2x+3

. (a) Obtain the quotient

q(x)

and the remainder

r(x)

when

p(x)

is divided by

d(x)

, expressing the coefficients of

r(x)

in terms of

k

. (b) If

x-1

is a factor of

p(x)

, determine the value of

k

. (c) For the value of

k

found in part (b), write the complete division statement that connects

p(x)

d(x)

, the corresponding quotient and the remainder.