It looks like you changed your guess for the final numerator from C to Cx+D. Cx+D is correct, since the discriminant of the denominator is

Thus, the denominator does not factor over the reals, and you need the Cx+D up top.

I think it should be

15A+25D+3B=-96. Other than that, I think you've set up your equations correctly.

Part (b) is way beyond me as well. It's an entirely different problem!?! Don't know why it's a part (b) to a partial fractions problem. I think an algebraist such as NonCommAlg or tonio or Swlabr would know what that's all about. Any chance you guys could weigh in on this?