The polynomial leaves a remainder of when divided by and is exactly divisible by

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

The polynomial

p(x)=2x^{3}+ax^{2}+bx-12

leaves a remainder of

6

when divided by

x-1

and is exactly divisible by

x+2

. Which pair

(a,b)

satisfies these conditions? (a)

a=9,\, b=8

(b)

a=11,\, b=5

(c)

a=10,\, b=6

(d)

a=8,\, b=2