The polynomial satisfies the following conditions: • The remainder when is divided by is

MATHEMATICS · Subjective · CBSE · Mathematics · Polynomials · Polynomials

Problem

The polynomial

P(x)=3x^{4}+ax^{3}+bx^{2}+cx+d

satisfies the following conditions: • The remainder when

P(x)

is divided by

(x-1)

-2

. • The remainder when

P(x)

is divided by

(x+1)

4

. • The remainder when

P(x)

is divided by

(x-2)

10

. •

(x+3)

is a factor of

P(x)

. (i) Translate each of the above statements into an equation involving

a, b, c,

and

d

. (ii) Solve the resulting system of four simultaneous equations to determine the values of

a, b, c,

and

d