grandes-ecoles 2024 Q7

grandes-ecoles · France · centrale-maths2__official Factor & Remainder Theorem Proof of Polynomial Divisibility or Identity
We denote by $\Delta_{d}$ the endomorphism of $\mathbb{K}_{d}[X]$ induced by $\Delta$, where $\Delta(P) = P(X+1) - P(X)$. Let $d \in \mathbb{N}^{*}$. Determine an annihilating polynomial of $\Delta_{d}$. Is the endomorphism $\Delta_{d}$ diagonalisable? 
We denote by $\Delta_{d}$ the endomorphism of $\mathbb{K}_{d}[X]$ induced by $\Delta$, where $\Delta(P) = P(X+1) - P(X)$. Let $d \in \mathbb{N}^{*}$. Determine an annihilating polynomial of $\Delta_{d}$. Is the endomorphism $\Delta_{d}$ diagonalisable?
Paper Questions
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