document.write( "Question 423063: what is the factor 7x^2-4x-11 \n" ); document.write( "

Algebra.Com's Answer #295184 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"7x%5E2-4x-11\"$ , we can see that the first coefficient is $\"7\"$ , the second coefficient is $\"-4\"$ , and the last term is $\"-11\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"7\"$ by the last term $\"-11\"$ to get $\"%287%29%28-11%29=-77\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-77\"$ (the previous product) and add to the second coefficient $\"-4\"$ ?\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 $\"-77\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-77\"$ :\r
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\n" ); document.write( "\n" ); document.write( "-1,-7,-11,-77\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 $\"-77\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-77) = -77
\n" ); document.write( "7*(-11) = -77
\n" ); document.write( "(-1)*(77) = -77
\n" ); document.write( "(-7)*(11) = -77\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 $\"-4\"$ :\r
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First Number	Second Number	Sum
1	-77	1+(-77)=-76
7	-11	7+(-11)=-4
-1	77	-1+77=76
-7	11	-7+11=4

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"7\"$ and $\"-11\"$ add to $\"-4\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"7\"$ and $\"-11\"$ both multiply to $\"-77\"$ and add to $\"-4\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-4x\"$ with $\"7x-11x\"$ . Remember, $\"7\"$ and $\"-11\"$ add to $\"-4\"$ . So this shows us that $\"7x-11x=-4x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"7x%5E2%2Bhighlight%287x-11x%29-11\"$ Replace the second term $\"-4x\"$ with $\"7x-11x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%287x%5E2%2B7x%29%2B%28-11x-11%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"7x%28x%2B1%29%2B%28-11x-11%29\"$ Factor out the GCF $\"7x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"7x%28x%2B1%29-11%28x%2B1%29\"$ Factor out $\"11\"$ 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( " $\"%287x-11%29%28x%2B1%29\"$ Combine like terms. Or factor out the common term $\"x%2B1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"7x%5E2-4x-11\"$ factors to $\"%287x-11%29%28x%2B1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"7x%5E2-4x-11=%287x-11%29%28x%2B1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%287x-11%29%28x%2B1%29\"$ to get $\"7x%5E2-4x-11\"$ 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( "Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you\r
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\n" ); document.write( "\n" ); document.write( "Jim \n" ); document.write( "

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