I have x^6 - 1=0

After the rational roots test, I have the factors of (x+1)(x-1).

So, after doing the synthetic division with these factors I am left with x^4 + x^2 + 1.

Now I am stuck. This equation does not factor, and it is not a quadratic. How do I move forward from here?

The roots by the way are 1,-1, and one plus or minus square root of 3 i divided by two and negative one plus or minus square root of 3 i divided by two. Please help!