Question

The polynomial g(x) = 2x³ + 3x² + qx - 1, has the same remainder when divided by ( x + 2 ) and ( x - 1 ). Find the value of constant q.

Answer 1

q = -3.

Explanation:

By the Remainder Theorem:

Remainder when dividing by x + 2 = g(-2) and

the remainder when dividing by x - 1 = g(1) .

So g(-2) = g(1) .

That is:

2(-2)^3 + 3(-2)^2 - 2q - 1 = 2(1)^3 + 3(1)^2 + q - 1

-16 + 12 - 2q - 1 = 2 + 3 + q - 1

-2q - q = 5 + 2 + 3 - 1

-3q = 9

q = -3.