document.write( "Question 560713: x^2 + 6x - 7 i am suppose to factor for x using area and i am lost. \n" ); document.write( "

Algebra.Com's Answer #364015 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"x%5E2%2B6x-7\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"6\"$ , and the last term is $\"-7\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"1\"$ by the last term $\"-7\"$ to get $\"%281%29%28-7%29=-7\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-7\"$ (the previous product) and add to the second coefficient $\"6\"$ ?\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 $\"-7\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-7\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,7\r
\n" ); document.write( "\n" ); document.write( "-1,-7\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 $\"-7\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-7) = -7
\n" ); document.write( "(-1)*(7) = -7\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 $\"6\"$ :\r
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First Number	Second Number	Sum
1	-7	1+(-7)=-6
-1	7	-1+7=6

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-1\"$ and $\"7\"$ add to $\"6\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-1\"$ and $\"7\"$ both multiply to $\"-7\"$ and add to $\"6\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"6x\"$ with $\"-x%2B7x\"$ . Remember, $\"-1\"$ and $\"7\"$ add to $\"6\"$ . So this shows us that $\"-x%2B7x=6x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bhighlight%28-x%2B7x%29-7\"$ Replace the second term $\"6x\"$ with $\"-x%2B7x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2-x%29%2B%287x-7%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x-1%29%2B%287x-7%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x-1%29%2B7%28x-1%29\"$ Factor out $\"7\"$ 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( " $\"%28x%2B7%29%28x-1%29\"$ 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 $\"x%5E2%2B6x-7\"$ factors to $\"%28x%2B7%29%28x-1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"x%5E2%2B6x-7=%28x%2B7%29%28x-1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%28x%2B7%29%28x-1%29\"$ to get $\"x%5E2%2B6x-7\"$ or by graphing the original expression and the answer (the two graphs should be identical).\r
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\n" ); document.write( "\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r
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\n" ); document.write( "\n" ); document.write( "Jim\r
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