HMMT 2015 Algebra #1

Let $Q$ be a polynomial $Q(x)=a_0 +a_1 x + \cdots + a_n x^n,$ where $a_0, \; \cdots,\; a_n$ are nonnegative integers. Given that $Q(1)=4$ and $Q(5)=152$, find $Q(6)$. 

정답 $254$