Polynomial q (1 Viewer)

[Sammy_b]

When a polynomial is divided by (2x + 1)(x - 3), the remainder is 3x - 1. What is the remainder when the polynomial is divided by 2x + 1?

This question's from Cambridge 3u, 4D q18.
Can anyone help?
Thanks.

 

[CM_Tutor]

If P(x) is the polynomial, then P(x) = (2x + 1)(x - 3)Q(x) + 3x - 1, where Q(x) is another polynomial.

The remainder on division by 2x + 1 is P(-1 / 2), by the remainder theorem.

P(-1 / 2) = [2(-1 / 2) + 1][(-1 / 2) - 3]Q(-1 / 2) + 3(-1 / 2) - 1 = 0 - (3 / 2) - 1 = -5 / 2

 

[Sammy_b]

Thank you!
They should really triple proof-read their answers in the back of the book! That was the answer i got, but the answers said 1/2.