document.write( "Question 189872: How do I factor this problem?\r
\n" ); document.write( "\n" ); document.write( "3m squared - 8m - 3 \n" ); document.write( "

Algebra.Com's Answer #142461 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"3m%5E2-8m-3\"$ , we can see that the first coefficient is $\"3\"$ , the second coefficient is $\"-8\"$ , and the last term is $\"-3\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"3\"$ by the last term $\"-3\"$ to get $\"%283%29%28-3%29=-9\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-9\"$ (the previous product) and add to the second coefficient $\"-8\"$ ?\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 $\"-9\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-9\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,3,9\r
\n" ); document.write( "\n" ); document.write( "-1,-3,-9\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 $\"-9\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-9)
\n" ); document.write( "3*(-3)
\n" ); document.write( "(-1)*(9)
\n" ); document.write( "(-3)*(3)\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 $\"-8\"$ :\r
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First Number	Second Number	Sum
1	-9	1+(-9)=-8
3	-3	3+(-3)=0
-1	9	-1+9=8
-3	3	-3+3=0

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"1\"$ and $\"-9\"$ add to $\"-8\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"1\"$ and $\"-9\"$ both multiply to $\"-9\"$ and add to $\"-8\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-8m\"$ with $\"m-9m\"$ . Remember, $\"1\"$ and $\"-9\"$ add to $\"-8\"$ . So this shows us that $\"m-9m=-8m\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"3m%5E2%2Bhighlight%28m-9m%29-3\"$ Replace the second term $\"-8m\"$ with $\"m-9m\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%283m%5E2%2Bm%29%2B%28-9m-3%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"m%283m%2B1%29%2B%28-9m-3%29\"$ Factor out the GCF $\"m\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"m%283m%2B1%29-3%283m%2B1%29\"$ 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( " $\"%28m-3%29%283m%2B1%29\"$ Combine like terms. Or factor out the common term $\"3m%2B1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"3m%5E2-8m-3\"$ factors to $\"%28m-3%29%283m%2B1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by FOILing $\"%28m-3%29%283m%2B1%29\"$ to get $\"3m%5E2-8m-3\"$ or by graphing the original expression and the answer (the two graphs should be identical).
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