Math Help - Polynomial functions.

1. Polynomial functions.

The expression 4x^3+ax^2-5x+b leaves remainders of -8 and 10 when divided by (2x-3) and (x-3) respectively. Calculate the values of a and b.
I've attempted this question a few times by trying to use the factor theorem and then rearranging the equations and subtracting them from each other. But, I couldn't get the right answer.
Thanks.

2. The Remainder Theorem

Let $F(x)=4x^3+ax^2-5x+b$

What you know so far is that $F(\frac{3}{2})=-8$, and that $F(3)=10$

Substituting into the polynomial gives:

$1) 4(\frac{3}{2})^3+a(\frac{3}{2})^2-5(\frac{3}{2})+b=-8$
$2) 4(3)^3+a(3)^2-5(3)+b=10$

Simplify, then solve for a and b. Post your working if you get stuck.