SOLUTION: Factor 1+x+x^2+x^3+x^4+x^5 as far as possible using only polynomials with integer coefficients. Show all work and explain how you got your answer.

Question 580852: Factor 1+x+x^2+x^3+x^4+x^5 as far as possible using only polynomials with integer coefficients. Show all work and explain how you got your answer.
Answer by KMST(5400) (Show Source): You can put this solution on YOUR website!
The only way I can think of factoring it is:

and there is no further factoring because the quadratic polynomials have no zeros:
and