How to factorize polynomial in GF(2)? I want to know how to factorize polynomials in $\ GF(2) $ without a calculator in a product of irreducible factors. For example, in my exercises, I must factorize $\ p(x) = (x^7 - 1)$
The response is $\ (x − 1)(x^3 + x^2 + 1)(x^3 + x + 1)$
I just not understand the methodology to do it just by hand. 
thanks a lot.

The methodology of factoring of a polynomial $f(x),$  $\deg f=n$:
1) find all irreducible polynomials up to degree $\dfrac{n}{2}.$
2) divide $f(x)$ on every of  the irreducible polynomials.
