Let . The polynomial leaves a remainder when divided by and is exactly divisible by .…

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Let

g(x)=2x^{3}+ax^{2}+bx-8

. The polynomial leaves a remainder

10

when divided by

x-2

and is exactly divisible by

x+3

. (a) Obtain two linear equations in

a

and

b

using the given information. (b) Solve these simultaneous equations to find the values of

a

and

b

. (c) Using the values of

a

and

b

, factorise

g(x)

completely. Provide complete working for each part.