Try a proof by contradiction for it...
This is similar to the Euclidian algorithm.
Prove the Following Lemma...:
Suppose p(x) and d(x) are polynomials in F[x] and that d(x) has degree at least 1. There exist unique polynomials q(x), r(x) E F(x) such that r(x) has lower degree than d(x) and
p(x) = q(x) . d(x) + r(x)
Please help..I have been struggling to understand this Lemma, but its quite complicated.