Not really a homework question, but I have a test tomorrow and I need to be able to solve these kind of problems.

Find the remainder when the polynomial $\displaystyle x^{100} + x^{67} - x^{32} - 2x^9 +1$ is divided with:

a) $\displaystyle x - 1$

b) $\displaystyle x + 2$

c) $\displaystyle x^2 - x$

I already have the answers, what I'm looking for is how to solve the problems. Polynomial long division would easily fill up several pages, so I'm clueless as what to do.

Thanks in advance!