document.write( "Question 787996: factor 2m^2-9m+4 \n" ); document.write( "

Algebra.Com's Answer #478372 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"2m%5E2-9m%2B4\"$ , we can see that the first coefficient is $\"2\"$ , the second coefficient is $\"-9\"$ , 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 $\"%282%29%284%29=8\"$ .\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 $\"-9\"$ ?\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 $\"-9\"$ :\r
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First Number	Second Number	Sum
1	8	1+8=9
2	4	2+4=6
-1	-8	-1+(-8)=-9
-2	-4	-2+(-4)=-6

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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 $\"-9\"$ (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 $\"-9\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-9m\"$ with $\"-m-8m\"$ . Remember, $\"-1\"$ and $\"-8\"$ add to $\"-9\"$ . So this shows us that $\"-m-8m=-9m\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"2m%5E2%2Bhighlight%28-m-8m%29%2B4\"$ Replace the second term $\"-9m\"$ with $\"-m-8m\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%282m%5E2-m%29%2B%28-8m%2B4%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"m%282m-1%29%2B%28-8m%2B4%29\"$ Factor out the GCF $\"m\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"m%282m-1%29-4%282m-1%29\"$ 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( " $\"%28m-4%29%282m-1%29\"$ Combine like terms. Or factor out the common term $\"2m-1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"2m%5E2-9m%2B4\"$ factors to $\"%28m-4%29%282m-1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"2m%5E2-9m%2B4=%28m-4%29%282m-1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%28m-4%29%282m-1%29\"$ to get $\"2m%5E2-9m%2B4\"$ or by graphing the original expression and the answer (the two graphs should be identical).
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