The polynomial leaves a remainder when divided by and a remainder when divided by

MATHEMATICS · Single correct · GCSE · Further Mathematics · Algebra and Proof · Algebra and Proof

Problem

The polynomial

p(x)=3x^{3}+kx^{2}+5x+m

leaves a remainder

4

when divided by

x-2

and a remainder

-5

when divided by

x+1

. Which ordered pair

(k,m)

satisfies these conditions? (a)

(11,\,-14)

(b)

(-9,\,12)

(c)

(-11,\,14)

(d)

(-9,\,6)