# Polynomials Proof

1. Apr 26, 2008

### JCIR

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. Apr 26, 2008

### HallsofIvy

Staff Emeritus
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.