document.write( "Question 154125: factorize x^3 -x^2 +ax+x-a - 1. thanks \n" ); document.write( "

Algebra.Com's Answer #113437 by jim_thompson5910(35256) $\"\"$ $\"About$

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$\"x%5E3+-x%5E2+%2Bax%2Bx-a+-+1\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E3+-x%5E2%29%2B%28ax-a%29%2B%28x+-+1%29\"$ Regroup the terms. This is not the only way to group them, but notice how the first two groups have something in common.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%28x-1%29%2Ba%28x-1%29%2B%28x-1%29\"$ Factor out the GCF $\"x%5E2\"$ from the first group. Factor out the GCF $\"a\"$ from the second group. \r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2Ba%2B1%29%28x-1%29\"$ Since we have the common term $\"x-1\"$ , we can combine like terms. Note:

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\n" ); document.write( "\n" ); document.write( "So $\"x%5E3+-x%5E2+%2Bax%2Bx-a+-+1\"$ factors to $\"%28x%5E2%2Ba%2B1%29%28x-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "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. \n" ); document.write( "

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