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How to factor (x^n-a^n)

  1. Oct 6, 2009 #1
    1. The problem statement, all variables and given/known data
    I would like to factor (x^n-a^n) such that (x^2-a^2) is one of the factors. Is this possible?


    2. Relevant equations



    3. The attempt at a solution
    I tried to get this with a kind of reverse polynomial long division, but couldn't do it.
     
  2. jcsd
  3. Oct 6, 2009 #2

    D H

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    This factoring is possible for some cases of n. It is not true in general. (x^2-a^2) is equal to (x-a)(x+a). It certainly is the case that (x-a) divides (x^n-a^n). What is the quotient? Under what circumstances does (x+a) divide this quotient?
     
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