Hello,

I've been working through a section on synthetic division, and in general have found it fairly comprehensible, having made few mistakes. That said, I'm having a hard time with the very last problem of the section. I've spent about an hour twisting it about, and can't figure out what I'm doing wrong. The answer, according to the book, is -9. However, I just can't figure out how to get there. Here is the problem:

Find the sum of a, b, c, and d if:

(x^3 - 2x^2 + 3x + 5)/(x+2) = ax^2 + bx + c + d/(x+2)

I figured since this is a synthetic division chapter that I should probably start there, so I used it on the left side of the problem to figure out, I think, that:

x^2 - 4x + 11 + 17/(x+2) = ax^2 + bx + c + d/(x+2)

I wasn't sure how to proceed from there, but tried multiplying both sides by (x+2) to get rid of the fractions:

(x+2)(x^2 - 4x + 11) + 17 = (x+2)(ax^2 + bx + c) + d

I'm not even sure that this is the right idea, or correct for that matter, and if it is, I still haven't been able to figure out how to remove x from the right of the problem to figure a+b+c+d. Clearly I'm missing something here, and any help in the right direction would be appreciated.