SOLUTION: please help! i am trying to factor 125x^(6) + 1. i have tried (5x^3)^3 + 1 but cannot get any further. thank you so much

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: please help! i am trying to factor 125x^(6) + 1. i have tried (5x^3)^3 + 1 but cannot get any further. thank you so much      Log On


   

Question 534928: please help! i am trying to factor 125x^(6) + 1. i have tried (5x^3)^3 + 1 but cannot get any further.
thank you so much
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
(5x^3)^3 = 125x^9. Your first step was incorrect.


125x^6 + 1 ---> (5x^2)^3 + 1


Set u=5x^2 so the equation becomes u^3+1.
The factor theorem states if f(a)=0 then x-a is a factor.


f(-1) = 0 --->-1^3+1=0. So u-1 is a factor.


(u-1)(u^2-u+1). (Substitute 5x^2 back in for u).


(5x^2-1)(25x^4-5x^2+1).