SOLUTION: factorize x^3 -x^2 +ax+x-a - 1. thanks

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Question 154125: factorize x^3 -x^2 +ax+x-a - 1. thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E3+-x%5E2+%2Bax%2Bx-a+-+1 Start with the given expression


%28x%5E3+-x%5E2%29%2B%28ax-a%29%2B%28x+-+1%29 Regroup the terms. This is not the only way to group them, but notice how the first two groups have something in common.


x%5E2%28x-1%29%2Ba%28x-1%29%2B%28x-1%29 Factor out the GCF x%5E2 from the first group. Factor out the GCF a from the second group.


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


So x%5E3+-x%5E2+%2Bax%2Bx-a+-+1 factors to %28x%5E2%2Ba%2B1%29%28x-1%29


If you want to, you can expand %28x%5E2%2Ba%2B1%29%28x-1%29 to get x%5E3+-x%5E2+%2Bax%2Bx-a+-+1 to verify your answer.