proof writing - Uniform continuity for a sequence of functions, $f_n (x)=x^n (1−x)$

I'm trying to prove the following.

Prove $f_n :[0,1] \rightarrow \Bbb R$ defined by $f_n (x)=x^n (1−x)$ converges uniformly to zero.

I know that for uniform continuity, we must find an $\varepsilon$ such that $|f_n(x)-0|

EDIT: I should mention that I am not allowed to use the derivative, we have not proven that in class yet.

I'm needing a little direction with this proof. Any help would be appreciated, thank you.