(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

How do you factorise polynomials in Z[x]? Z is not a field so you can't use the theorem 'a is a root of f <=> (x-a) divides f'

3. The attempt at a solution

Would you map the polynomials from Z[x] to Q[x] by multiplying by 1, since all elements in Z[x] are in Q[x]. Then factorise in Q[x] usiong the theorem above. If the factors have coefficients in Z than map (multiply by 1) these back to Z[x] so you have factorised these polynomials and they exist in Z[x]. If the factors in Q[x] have coefficients not in Z then you can't map back to Z[x] hence these are not factorisable in Z[x].

Is this how you would factorise polynomials in Z[x], formally?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Factorise elements in Z[x]?

**Physics Forums | Science Articles, Homework Help, Discussion**