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Homework Help: Polynomials Proof

  1. Apr 26, 2008 #1
    1. The problem statement, all variables and given/known data
    For polynomials over a field F, prove that every non constant polynomial can be expressed as a product of irreducible polynomial.


    2. Relevant equations
    No relevant equations.


    3. The attempt at a solution
    Well a hint the teacher gave me was that the degree of the irreducible polynomial
    has to be the same as the original polynomial.
     
  2. jcsd
  3. Apr 26, 2008 #2

    HallsofIvy

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    Science Advisor

    Surely you misunderstood. I have no idea what you mean by "the irreducible polynomial" since you are talking about a product of such things and there will generally be more than one. Also the total degree must be equal to the pdegree of the original polynomial. For example x2- a2= (x- a)(x+ a) is a second degree polynomial that is the product of two first degree irreducible polynomials.

    Start with the definitions of "reducible" and "irreducible".
     
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