Prove that f_{n}(x) = n^{2}x^{2}e^{-nx}converges uniformly on [1, inf). I have to use epsilon proof.

I have found the point-wise limit f(x) = 0. I let e > 0. So far I have bounded n^{2}x^{2}e^{-nx}< n^{2}x^{2}e^{-n}. I can't seem to eliminate this x^{2}. Any hints? Thanks.