Find the partial fractions for the following:

3x² - 2x + 8

------------------------

x³ + 2x² + 4x + 8

9x² + 21x - 24

--------------------------

x³ + 4x² - 11x - 30

My biggest problem with these is that I have trouble factoring the bottom cubic in the second problem, but I'm having trouble with everything else also. Every time I try to solve the problems I end up with a different answer than the time before. I don't know what I am doing wrong!

I shall be eternally grateful to whoever helps me solve these problems. So grateful, in fact, that I shall bestow upon them this bear hug.

. . . Wow. It's obviously sleepy time for me. My true weirdness is oozing into your website. Terribly sorry about that.