SOLUTION: Factor Each expression: x^3 +x^2 -x -1

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Question 119398: Factor Each expression:
x^3 +x^2 -x -1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E3%2Bx%5E2-x-1 Start with the given expression

%28x%5E3%2Bx%5E2%29%2B%28-x-1%29 Group like terms


x%5E2%28x%2B1%29-1%28x%2B1%29 Factor out the GCF x%5E2 out of the first group. Factor out the GCF -1 out of the second group


%28x%5E2-1%29%28x%2B1%29 Since we have the common term x%2B1, we can combine like terms


%28x-1%29%28x%2B1%29%28x%2B1%29 Now factor x%5E2-1 by using the difference of squares



%28x-1%29%28x%2B1%29%5E2 Multiply



So x%5E3%2Bx%5E2-x-1 factors to %28x-1%29%28x%2B1%29%5E2