I was hoping someone could give me a hand with this little problem that's been driving me a bit nuts:

Show that there is a factorization x = f(x)g(x) in Z_4[x] (the polynomial ring over the integers mod 4) such that neither f(x) nor g(x) is a constant.

Is there some kind of method or good way to find these factors, or is it just a guess and check situation? I've been searching for these factors for a while with no luck (haven't strayed beyond quadratics yet).