Let $n$ be a non-zero natural number. Let $P$ be in $\mathbb{C}_{2n}[X]$, and, for all $\lambda \in \mathbb{C}$, $P_\lambda(X) = P(\lambda X) - P(\lambda)$. If $\lambda \in \mathbb{C}$, verify that $X - 1$ divides $P_\lambda$.
Let $n$ be a non-zero natural number. Let $P$ be in $\mathbb{C}_{2n}[X]$, and, for all $\lambda \in \mathbb{C}$, $P_\lambda(X) = P(\lambda X) - P(\lambda)$.
If $\lambda \in \mathbb{C}$, verify that $X - 1$ divides $P_\lambda$.