Determine $\displaystyle g(x)\equiv (px+q)^2(2x^2-5x-3)$ where p,q are constants, given that, on division by $\displaystyle (x-2)^2$, the remainder is $\displaystyle -39-3x$.

I found

$\displaystyle g(2)=(2p+q)^2(-5)=-45$

$\displaystyle (2p+q)^2=9$

$\displaystyle 2p+q=\pm 3$

I don't think I'm on the right track, but I don't know how else to work it out.

Thanks!