Prove: Non-constant Polynomials as Products of Irreducibles

[JCIR]

Homework Statement

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

Homework Equations

No relevant equations.

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.

 

[HallsofIvy]

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".