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MathNet 2012 Question 51

Math Olympiad Vault · MathNet 2012

Question 51

Let $Q(x)=x^2+2x+3$, and suppose that $P(x)$ is a polynomial such that
$$\begin{aligned}P(Q(x))={}&x^6+6x^5+18x^4+32x^3\\&+35x^2+22x+8.\end{aligned}$$
Compute $P(2)$.