I'm getting a slightly different answer: I don't come up with the $\displaystyle x^2$, but I've got everything else. Any ideas what I could have missed?

I went the $\displaystyle 2x^3-4x^2-15x+5=A(x-4)+B(x+2)$ route and got $\displaystyle A=\frac{-1}{2}$ and $\displaystyle B=\frac{3}{2}$.