Stewart Mckenzie
04/12/2023 · Elementary School
Exercice 4.3. Soit \( a \in \mathbb{K} \) et \( P \in \mathbb{K}[X] \). Exprimer le reste de la division euclidienne de \( P \operatorname{par}(X-a)^{2} \) en fonction de \( P(a) \) et \( P^{\prime}(a) \). Exercice 4.4. Soit \( n \in \mathbb{N} \). Montrer que \( 1-X \) divise \( 1-X^{n+1} \) dans \( \mathbb{K}[X] \) et donner
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Pour l'exercice 4.3, le reste de la division euclidienne de \( P \) par \( (X-a)^{2} \) est \( P(a) \).
Pour l'exercice 4.4, \( 1-X \) divise \( 1-X^{n+1} \) dans \( \mathbb{K}[X] \).
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