Suppose f is an entire function that satisfies $\displaystyle |f(z)|\leq M(1+|z|^m) $ for some constant M and positive integer m. Show that f is a polynomial of at most degree m.

How should I approach this? Do I try to bound $\displaystyle |\frac{f(z)} {1+z^m}| $, and then apply Liouville's theorem? The expression isn't necessarily entire though.