We are given a polynomial $P \in \mathbb{C}[X]$ of degree $d$. Show that, for all $z \in \mathbb{C}$:
$$|P(z)| \leq \|P\|_{\partial\mathbb{D}} \max\{1, |z|\}^d.$$
One may apply question 3.18 to the polynomials $P(X)$ and $Q(X) = X^d P\left(X^{-1}\right)$.