to find primitive roots of a galois field

Question

I need to find the members of Galois Field with $p = 11$. I proceeded in this way:
$x^{10} - 1 = 0 $

implies $\frac{(x^{10}-1)}{(x+1)(x^{5}-1)} = 0 $ which implies $x^{4} - x^{3} + x^{2} - x + 1 =0$

Now I am stuck as I am not being able to reduce this polynomial.How to find it's roots?