SOLUTION: Please Help! Factor x^8-1 This problem seems simple, but is making my head spin!! Thank you!!!

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Question 622008: Please Help! Factor
x^8-1 This problem seems simple, but is making my head spin!! Thank you!!!
Answer by KMST(5396) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E8-1=%28x%5E4%29%5E2-1=%28x%5E4%2B1%29%28x%5E4-1%29 for starters.
x%5E4%2B1=0 does not have real solutions, so you cannot factor x%5E4%2B1
However,
x%5E4-1=%28x%5E2%29%5E2-1=%28x%5E2%2B1%29%28x%5E2-1%29
x%5E2%2B1=0 does not have real solutions, so you cannot factor x%5E2%2B1
However,
x%5E2-1=%28x%2B1%29%28x-1%29
Putting it all together, you get to the full factorization in a few steps