Question 8
Let $P(x)$, $Q(x)$, $R(x)$ and $S(x)$ be non-constant polynomials with real coefficients such that $P(Q(x)) = R(S(x))$. Prove that, if the degree of $P(x)$ is divisible by the degree of $R(x)$, then $P(x) = R(T(x))$ for some polynomial $T(x)$ with real coefficients.