HMMT November 2012 E2

Let $Q(x)=x^{2}+2 x+3$, and suppose that $P(x)$ is a polynomial such that

$$P(Q(x))=x^{6}+6 x^{5}+18 x^{4}+32 x^{3}+35 x^{2}+22 x+8$$

Compute $P(2)$.