document.write( "Question 878516: how do you foil 7x^2+16x-15
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Algebra.Com's Answer #530026 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"7x%5E2%2B16x-15\"$ , we can see that the first coefficient is $\"7\"$ , the second coefficient is $\"16\"$ , and the last term is $\"-15\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"7\"$ by the last term $\"-15\"$ to get $\"%287%29%28-15%29=-105\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-105\"$ (the previous product) and add to the second coefficient $\"16\"$ ?\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 $\"-105\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-105\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,3,5,7,15,21,35,105\r
\n" ); document.write( "\n" ); document.write( "-1,-3,-5,-7,-15,-21,-35,-105\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 $\"-105\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-105) = -105
\n" ); document.write( "3*(-35) = -105
\n" ); document.write( "5*(-21) = -105
\n" ); document.write( "7*(-15) = -105
\n" ); document.write( "(-1)*(105) = -105
\n" ); document.write( "(-3)*(35) = -105
\n" ); document.write( "(-5)*(21) = -105
\n" ); document.write( "(-7)*(15) = -105\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 $\"16\"$ :\r
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First Number	Second Number	Sum
1	-105	1+(-105)=-104
3	-35	3+(-35)=-32
5	-21	5+(-21)=-16
7	-15	7+(-15)=-8
-1	105	-1+105=104
-3	35	-3+35=32
-5	21	-5+21=16
-7	15	-7+15=8

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-5\"$ and $\"21\"$ add to $\"16\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-5\"$ and $\"21\"$ both multiply to $\"-105\"$ and add to $\"16\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"16x\"$ with $\"-5x%2B21x\"$ . Remember, $\"-5\"$ and $\"21\"$ add to $\"16\"$ . So this shows us that $\"-5x%2B21x=16x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"7x%5E2%2Bhighlight%28-5x%2B21x%29-15\"$ Replace the second term $\"16x\"$ with $\"-5x%2B21x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%287x%5E2-5x%29%2B%2821x-15%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%287x-5%29%2B%2821x-15%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%287x-5%29%2B3%287x-5%29\"$ 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( " $\"%28x%2B3%29%287x-5%29\"$ Combine like terms. Or factor out the common term $\"7x-5\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"7x%5E2%2B16x-15\"$ factors to $\"%28x%2B3%29%287x-5%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"7x%5E2%2B16x-15=%28x%2B3%29%287x-5%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%28x%2B3%29%287x-5%29\"$ to get $\"7x%5E2%2B16x-15\"$ or by graphing the original expression and the answer (the two graphs should be identical).
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