Is the endomorphism $P(X)\mapsto P(X+1)-P(X)$ diagonalizable?

Let $n\in \mathbb{N}$, $n\ge 2$. Is the endomorphism $\varphi$ of $\mathbb{C}_n[X]$, which maps the polynomial $P(X)$ to the polynomial $P(X+1)-P(X)$, diagonalizable?

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Linear Algebra · Fundemental Theorem of Algebra · Diagonalization