O-level A-Maths Remainder Theorem Problem

Hi, I am not sure how do I solve this question:

When 2x^3 - 4x^2 - 5x - 2 is divided by (x-1)(x+2), the remainder is ax+b. This result may be expressed as the identity

2x^3 - 4x^2 - 5x - 2 = (x-1)(x+2)Q(x) + ax+b

where Q(x) is the quotient.

a) State the degree of Q(x).

b) By Substituting suitable values of x, find a and b

Solutions:

a) 1

b) a=5, b=-14

Hi,

(a) A cubic expression (of degree 3) is divided by a quadratic expression (of degree 2), so we will obtain a linear expression (whose degree is 1).

(b) An obvious set of substitutions is x = 1 and x = -2, since we are already given a convenient identity.

An alternative approach would be to carry out long division directly to obtain the exact quotient and remainder expressions.

Cheers,
Wen Shih

it is solved, thanks for your help :)