While studying about the galois field $GF(2)[x]$, i wanted to find out whether a given polynomial is primitive or not. To do that i need to factor this term:
$x^8 - x$.
I got the only solution that it is equals to $x(x−1)(x^3+x+1)(x^3+x^2+1)$ but no explaination how to do that.
How can i factor the expression : $x^8 - x$ to the corresponding polynomials product?What is the procedure?
Factor out the $x$, then $x - 1$. The roots of the quotient occur in conjugate pairs. Each pair yields up an irreducible (over the reals) quadratic.