How do you factor x^3 + x^2 + x + 1 ??? I need complex answers too. Help would be greatly appreciated.

Factor the following:
x^3+x^2+x+1

 

Factor terms by grouping. x^3+x^2+x+1 = (x^3+x^2)+(x+1) = x^2 (x+1)+(x+1):
x^2 (x+1)+(x+1)

 

Factor x+1 from x^2 (x+1)+(x+1):
Answer: |  (x+1) (x^2+1)    and complex factors: (x-i) (x+i) (x+1)