For every polynomial $P = P(X) \in \mathbf{C}_{n-1}[X]$ we set
$$\left\{\begin{array}{l} s_1(P) = P(-X) \\ s_2(P) = P(1-X) \\ g(P) = P(X+1) - P(X) \end{array}\right.$$
We thus define three endomorphisms of the vector space $\mathbb{C}_{n-1}[X]$.
Calculate $s_1^2$, $s_2^2$ and express $s_1 \circ s_2$ in terms of $g$ and $Id_{\mathbb{C}_{n-1}[X]}$.