Let p(x)=2x^ 3 +ax^ 2 +bx-18

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

Problem

Let

p(x)=2x^{3}+ax^{2}+bx-18.

The polynomial is divided by two different linear polynomials with the following results: • When divided by

x+1

, the remainder is

0

. • When divided by

x-2

, the remainder is

6

. Answer the questions below. (i) Form two separate equations in

a

and

b

using the above information. (ii) Solve the simultaneous equations to find the values of

a

and

b

. (iii) Using the values of

a

and

b

, find the remainder obtained when

p(x)

is divided by

x+3