# Roots of polynomial

I want to show that every polynomial of degree 1, 2 and 4 in Z_2[x] has a root in Z_2[x]/(x^4+x+1). Any ideas?

Ps. How can I use latex commands in my posts?

matt grime
Homework Helper
You can just do it by exhaustion. There are very few cases to think about (and if you have to start thinking about the case deg=1 then you're missing something).

LaTeX is explained in the introduction to LaTeX thread (probably in physics): just look around.

Okey, something like this?
The case deg 1 is obvious. The case 2 is obvious except for the irreducible x^2+x+1, where I can find a solution. Degree 4 is obvious except for the irreducible cases which I can try?

Im not really satsified with this solution.

matt grime