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Unique Factorization for polynomials

  1. Jun 20, 2010 #1
    1. The problem statement, all variables and given/known data
    Prove unique factorization for hte set of polynomials in x with integer coefficients


    2. Relevant equations
    The Euclidean algorithm may be of some use


    3. The attempt at a solution
    Let's say that the polynomial is of the form anx^n + a(n-1)x^(n-1) ... a1x + a0

    There are only n values of x not necessarily distinct so that the polynomial equals 0. If one of these values of x is p, then (x-p) divides the polynomial.

    It's a more of a gut feeling/intuition thing that I need to prove using logic and actual theorems
     
  2. jcsd
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