Abstract Algebra #36 Only please

220 Part IV Rings and Fields 36. (Remainder Theorem) Let f(x) e F[x] where F is a field, and let a e F. Show that the remainder r(x) when f(x) is divided by x - a, in accordance with the division algorithm, is f(o). 37. Let Om : Z - Zm be the natural homomorphism given by om(a) = (the remainder of a when divided by m) for a E Z