Are the following polynomials irreducible over Z2?

[krispiekr3am]

Are the following polynomials irreducible over Z2?

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

 

[Hurkyl]

Have you had any thoughts on the problem?

 

[HallsofIvy]

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".