We choose $I = [-1,1]$ and write $C_{n,m}$ instead of $C_{n,m}^I$. Let $(Q_2, R_2)$ be a good extremal pair. Let $w$ be a root of $Q_2$ and let $S \in \mathbb{C}[X]$ be such that:
$$Q_2(X) = (X - w)S(X)$$
By setting:
$$S_2(X) = (X + 1 - |w+1|)S(X)$$
show that $(S_2, R_2)$ is a good extremal pair.