For every polynomial $P = P(X) \in \mathbf{C}_{n-1}[X]$ we set $$g(P) = P(X+1) - P(X)$$ Let $P$ be a non-constant polynomial. Express the degree of the polynomial $g(P)$ in terms of the degree of $P$.
For every polynomial $P = P(X) \in \mathbf{C}_{n-1}[X]$ we set
$$g(P) = P(X+1) - P(X)$$
Let $P$ be a non-constant polynomial. Express the degree of the polynomial $g(P)$ in terms of the degree of $P$.