Show that $\Delta$ is an endomorphism of $\mathbb{K}[X]$, where $$\Delta : \begin{cases} \mathbb{K}[X] \rightarrow \mathbb{K}[X] \\ P(X) \mapsto P(X+1) - P(X) \end{cases}$$
Show that $\Delta$ is an endomorphism of $\mathbb{K}[X]$, where
$$\Delta : \begin{cases} \mathbb{K}[X] \rightarrow \mathbb{K}[X] \\ P(X) \mapsto P(X+1) - P(X) \end{cases}$$