We fix two non-zero natural integers $n$ and $m$ as well as two polynomials $Q \in \mathbb{C}[X]$ and $R \in \mathbb{C}[X]$ of degrees $n$ and $m$ respectively. We introduce the polynomial $P = QR$. We set $C = \exp\left(\frac{I}{2\pi}\right)$ with:
$$I = \int_0^{2\pi} \ln\left(\max\left\{\left|e^{i\theta} - 1\right|, \left|e^{i\theta} + 1\right|\right\}\right) d\theta$$
Using the previous questions, show that:
$$\|Q\|_{\mathbb{D}} \|R\|_{\mathbb{D}} \leq C^{n+m} \|P\|_{\mathbb{D}}$$