Challenge factoring problem.?

Question

If you want to tackle a challenge factoring problem then I think you may find this one fun. First correct answer will get the 10.

Completely factor:

x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x +1

I should have pointed out that I was looking for non-Complex factoriztion, but if you want to factor to complex roots that would be fine, too. Not required to be best answer though...

Answer 1

x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x +1

(x^8 + x^7 + x^6 )+ (x^5 + x^4 + x^3) +( x^2 + x +1)

x^6(x^2 + x + 1) + x^3(x^2 + x + 1) + 1(x^2 + x + 1)

(x^2 + x + 1) (x^6 + x^3 + 1)

that's the furthest you can go