Let f(x) be a polynomial of degree n. c(sub 0)x^0 + ... + c(sub n)x^n

I need to prove that if n >= 1 and f(a) = 0 from some real a, then f(x) = (x - a)h(x) where h is a polynomial of degree n - 1. The book i'm using (calculus vol 1 by Apostol) gives the hint: "consider p(x) = f(x + a)" - but I still can't come up with a proof.