SOLUTION: how do you factor the polynomial x^4-8x^2-9

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Question 256125: how do you factor the polynomial x^4-8x^2-9
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
We are given
(i) x%5E4-8x%5E2-9
step 1 - set up a dummy variable like U = x^2. If U = x^2, then U^2 = x^4.
Step 2 - substitute the dummy variable into the equation to get
(ii) U%5E2+-8U+-9
step 3 - factoring we get
(iii) %28U-9%29%28U%2B1%29
step 4 - replace U with x^2 to get
(iv)%28x%5E2-9%29%28x%5E2%2B1%29
step 5 - notice the difference of squares. We can factor that to get
(v) %28x-3%29%28x%2B3%29%28x%5E2%2B1%29