## How to factor a polynomial modulo p?

I can understand most of Galois Theory and Number Theory dealing with factorization and extension fields, but I always run into problems that involve factorization mod p, which I can't seem to figure out how to do. I can't find any notes anywhere either, so I was wondering if someone could give me some steps. p is prime, of course.
 Recognitions: Homework Help Science Advisor Do you have any specific questions? For general reading material, you could try googling "factoring polynomials over finite fields".

 Quote by morphism Do you have any specific questions? For general reading material, you could try googling "factoring polynomials over finite fields".
I seem to have figured out how to factor mod p (in a prime field) between a couple documents:

www.science.unitn.it/~degraaf/compalg/polfact.pdf

http://www.math.uiuc.edu/~r-ash/Ant/AntChapter4.pdf

However, I'm still wondering what other types of finite fields it would be useful to factor over (am I correct in assuming that not all finite fields are prime fields?)

## How to factor a polynomial modulo p?

You usually reduce the polynomial using the small Fermat theorem, xp $\equiv$ x (mod p) for every variable x that has a power greater than p-1