SOLUTION: how do you factor x to the sixth power plus one

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Question 635918: how do you factor x to the sixth power plus one
Answer by KMST(5396) About Me  (Show Source):
You can put this solution on YOUR website!
To factor x%5E6%2B1 , I would think of
y%5E3%2B1=%28y%2B1%29%28y%5E2-y%2B1%29 , which is a full factorization,
because if y%5E2-y%2B1 had factors (with real coefficients),
y%5E2-y%2B1=0 would have real solutions (and it does not).
If we make y=x%5E2 in y%5E3%2B1=%28y%2B1%29%28y%5E2-y%2B1%29 , we get
highlight%28x%5E6%2B1=%28x%5E2%2B1%29%28x%5E4-x%5E2%2B1%29%29