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.

Algebra ->  Polynomials-and-rational-expressions -> 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.      Log On


   

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(5399) About Me  (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:
x%5E2%2Bx%2B1%3Ex%5E2%2Bx%2B1%2F4=%28x%2B1%2F2%29%5E2%3E=0 and
x%5E2-x%2B1%3Ex%5E2-x%2B1%2F4=%28x-1%2F2%29%5E2%3E=0