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let-p-K-n-x-snd-A-and-H-two-rlements-of-K-x-1-prove-that-p-A-x-H-x-k-0-n-p-k-A-x-k-H-x-k-2-find-the-condition-that-p-A-x-H-x-is-divided-by-H-x-0-3-if-p-x-c-prove-t

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Question Number 50363 by prof Abdo imad last updated on 16/Dec/18
let p ∈K_n [x] snd A and H two rlements of K[x] 1) prove that p(A(x)+H(x))=Σ_(k=0) ^n ((p^((k)) (A(x)))/(k!)).(H(x))^k 2)find the condition that p(A(x)+H(x))is divided by H(x)≠0 3) if p(x)≠c prove that p(p(x))−x is divided by p(x)−x.
letp∈Kn[x]sndAandHtworlementsofK[x]1)provethatp(A(x)+H(x))=∑k=0np(k)(A(x))k!.(H(x))k2)findtheconditionthatp(A(x)+H(x))isdividedbyH(x)≠03)ifp(x)≠cprovethatp(p(x))−xisdividedbyp(x)−x.

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