SOLUTION: Factor if possible: x^5 - 6x^3 + 5x

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Question 256186: Factor if possible: x^5 - 6x^3 + 5x
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
We start with
x%5E5+-+6x%5E3+%2B+5x
factor out an x to get
x%28x%5E4+-+6x%5E2+%2B+5%29
Let U = x^2 and U^2 = x^4. By substitution, we get
x%28U%5E2+-+6U+%2B+5%29
factored, we get
x%28U%2B5%29%28U%2B1%29
resubbing x^2 for U, we get
x%28x%5E2%2B5%29%28x%5E2%2B1%29