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Math Help - monic polynomials

  1. #1
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    monic polynomials

    Any ideas on this one?

    Let f(x) be a monic polynomial over Z. Show that if n is a nonzero integer such that f(n) = 0, then n divides f(0).

    Thanks!
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  2. #2
    Super Member Gamma's Avatar
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    f(x)=x^k + a_{k-1}x^{k-1} + ... + a_1x + a_0
    f(n)=n^k + a_{k-1}n^{k-1} + ... + a_1n + a_0=0
    n^k + a_{k-1}n^{k-1} + ... + a_1n =- a_0
    n divides the left side, so n divides a_0=f(0)
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  3. #3
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    Quote Originally Posted by hka210 View Post
    Any ideas on this one?

    Let f(x) be a monic polynomial over Z. Show that if n is a nonzero integer such that f(n) = 0, then n divides f(0).

    Thanks!
    If f(n)= 0, then (x- n) is a factor of f(x).
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