document.write( "Question 168692: Factor\r
\n" ); document.write( "\n" ); document.write( "4m^2-8m+3 \n" ); document.write( "

Algebra.Com's Answer #124361 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"4m%5E2-8m%2B3\"$ , we can see that the first coefficient is $\"4\"$ , 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 $\"4\"$ by the last term $\"3\"$ to get $\"%284%29%283%29=12\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"12\"$ (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 $\"12\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"12\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,12\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-12\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 $\"12\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*12
\n" ); document.write( "2*6
\n" ); document.write( "3*4
\n" ); document.write( "(-1)*(-12)
\n" ); document.write( "(-2)*(-6)
\n" ); document.write( "(-3)*(-4)\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	12	1+12=13
2	6	2+6=8
3	4	3+4=7
-1	-12	-1+(-12)=-13
-2	-6	-2+(-6)=-8
-3	-4	-3+(-4)=-7

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-2\"$ and $\"-6\"$ add to $\"-8\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-2\"$ and $\"-6\"$ both multiply to $\"12\"$ and add to $\"-8\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-8m\"$ with $\"-2m-6m\"$ . Remember, $\"-2\"$ and $\"-6\"$ add to $\"-8\"$ . So this shows us that $\"-2m-6m=-8m\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"4m%5E2%2Bhighlight%28-2m-6m%29%2B3\"$ Replace the second term $\"-8m\"$ with $\"-2m-6m\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%284m%5E2-2m%29%2B%28-6m%2B3%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"2m%282m-1%29%2B%28-6m%2B3%29\"$ Factor out the GCF $\"2m\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"2m%282m-1%29-3%282m-1%29\"$ 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( " $\"%282m-3%29%282m-1%29\"$ 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 $\"4m%5E2-8m%2B3\"$ factors to $\"%282m-3%29%282m-1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by FOILing $\"%282m-3%29%282m-1%29\"$ to get $\"4m%5E2-8m%2B3\"$ or by graphing the original expression and the answer (the two graphs should be identical).
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