SOLUTION: factor x^5 - 1

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Question 390481: factor
x^5 - 1
Found 2 solutions by edjones, richard1234:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
x^5 - 1
x^n - y^n is always divisible by x - y, so x^5 - 1 has x - 1 as a factor.
x^5-1/(x-1)=x^4+x^3+x^2+x+1 Long division.
(x-1)(x^4+x^3+x^2+x+1)
.
Ed

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
A neat shortcut:

If you know that the sum of a geometric sequence

x+%2B+x%5E2+%2B+x%5E3 + ... + x%5En is %28x%5E%28n%2B1%29+-+1%29%2F%28x-1%29 we can obtain

x+%2B+x%5E2+%2B+x%5E3+%2B+x%5E4+=+%28x%5E5+-+1%29%2F%28x-1%29

Multiplying both sides by x-1, we get the factorization of x%5E5+-+1

x%5E5+-+1+=+%28x+%2B+x%5E2+%2B+x%5E3+%2B+x%5E4%29%28x-1%29