Polynomials Proof

  • Thread starter JCIR
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Homework Statement


For polynomials over a field F, prove that every non constant polynomial can be expressed as a product of irreducible polynomial.


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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.
 

Answers and Replies

  • #2
HallsofIvy
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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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