document.write( "Question 416125: Factor the trinomial: 2n^2 - 7n - 4 \n" ); document.write( "

Algebra.Com's Answer #291601 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"2n%5E2-7n-4\"$ , we can see that the first coefficient is $\"2\"$ , the second coefficient is $\"-7\"$ , and the last term is $\"-4\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"2\"$ by the last term $\"-4\"$ to get $\"%282%29%28-4%29=-8\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-8\"$ (the previous product) and add to the second coefficient $\"-7\"$ ?\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 $\"-8\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-8\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,4,8\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-8\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 $\"-8\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-8) = -8
\n" ); document.write( "2*(-4) = -8
\n" ); document.write( "(-1)*(8) = -8
\n" ); document.write( "(-2)*(4) = -8\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 $\"-7\"$ :\r
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First Number	Second Number	Sum
1	-8	1+(-8)=-7
2	-4	2+(-4)=-2
-1	8	-1+8=7
-2	4	-2+4=2

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"1\"$ and $\"-8\"$ add to $\"-7\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"1\"$ and $\"-8\"$ both multiply to $\"-8\"$ and add to $\"-7\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-7n\"$ with $\"n-8n\"$ . Remember, $\"1\"$ and $\"-8\"$ add to $\"-7\"$ . So this shows us that $\"n-8n=-7n\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"2n%5E2%2Bhighlight%28n-8n%29-4\"$ Replace the second term $\"-7n\"$ with $\"n-8n\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%282n%5E2%2Bn%29%2B%28-8n-4%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"n%282n%2B1%29%2B%28-8n-4%29\"$ Factor out the GCF $\"n\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"n%282n%2B1%29-4%282n%2B1%29\"$ Factor out $\"4\"$ 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( " $\"%28n-4%29%282n%2B1%29\"$ Combine like terms. Or factor out the common term $\"2n%2B1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"2n%5E2-7n-4\"$ factors to $\"%28n-4%29%282n%2B1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"2n%5E2-7n-4=%28n-4%29%282n%2B1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%28n-4%29%282n%2B1%29\"$ to get $\"2n%5E2-7n-4\"$ 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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