# Are the following polynomials irreducible over Z2?

1. Nov 7, 2006

### krispiekr3am

Are the following polynomials irreducible over Z2?

(a) x2 + x + 1
(b) x2 + 1
(c) x2 + x

2. Nov 7, 2006

### Hurkyl

Staff Emeritus
Have you had any thoughts on the problem?

3. Nov 8, 2006

### HallsofIvy

Staff Emeritus
Z2 only has 2 elements. Have you checked to see what each of them gives in these polynomials? Finding the roots of p(x)= 0 is often a good way to factor the polynomial p(x)!

And please write at least x^2 for x2, not "x2".

Last edited: Nov 8, 2006