document.write( "Question 214534This question is from textbook blitzer college algebra essential
\n" ); document.write( ": factor x^2+2x-3 \n" ); document.write( "

Algebra.Com's Answer #162042 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"x%5E2%2B2x-3\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"2\"$ , and the last term is $\"-3\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"1\"$ by the last term $\"-3\"$ to get $\"%281%29%28-3%29=-3\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-3\"$ (the previous product) and add to the second coefficient $\"2\"$ ?\r
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\n" ); document.write( "\n" ); document.write( "To find these two numbers, we need to list all of the factors of $\"-3\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-3\"$ :\r
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\n" ); document.write( "\n" ); document.write( "Note: list the negative of each factor. This will allow us to find all possible combinations.\r
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\n" ); document.write( "\n" ); document.write( "These factors pair up and multiply to $\"-3\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-3) = -3
\n" ); document.write( "(-1)*(3) = -3\r
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\n" ); document.write( "\n" ); document.write( "Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"2\"$ :\r
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First Number	Second Number	Sum
1	-3	1+(-3)=-2
-1	3	-1+3=2

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-1\"$ and $\"3\"$ add to $\"2\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-1\"$ and $\"3\"$ both multiply to $\"-3\"$ and add to $\"2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"2x\"$ with $\"-x%2B3x\"$ . Remember, $\"-1\"$ and $\"3\"$ add to $\"2\"$ . So this shows us that $\"-x%2B3x=2x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bhighlight%28-x%2B3x%29-3\"$ Replace the second term $\"2x\"$ with $\"-x%2B3x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2-x%29%2B%283x-3%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x-1%29%2B%283x-3%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x-1%29%2B3%28x-1%29\"$ Factor out $\"3\"$ from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B3%29%28x-1%29\"$ Combine like terms. Or factor out the common term $\"x-1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E2%2B2x-3\"$ factors to $\"%28x%2B3%29%28x-1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"x%5E2%2B2x-3=%28x%2B3%29%28x-1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%28x%2B3%29%28x-1%29\"$ to get $\"x%5E2%2B2x-3\"$ or by graphing the original expression and the answer (the two graphs should be identical).\r
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