document.write( "Question 117557: factor the following\r
\n" ); document.write( "\n" ); document.write( "m^2+3m-28 \n" ); document.write( "

Algebra.Com's Answer #85541 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at $\"m%5E2%2B3m-28\"$ we can see that the first term is $\"m%5E2\"$ and the last term is $\"-28\"$ where the coefficients are 1 and -28 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient -28 to get -28. Now what two numbers multiply to -28 and add to the middle coefficient 3? Let's list all of the factors of -28:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -28:\r
\n" ); document.write( "\n" ); document.write( "1,2,4,7,14,28\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-7,-14,-28 ...List the negative factors as well. 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 -28\r
\n" ); document.write( "\n" ); document.write( "(1)*(-28)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-14)\r
\n" ); document.write( "\n" ); document.write( "(4)*(-7)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(28)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(14)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(7)\r
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\n" ); document.write( "\n" ); document.write( "note: remember, the product of a negative and a positive number is a negative number\r
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\n" ); document.write( "\n" ); document.write( "Now which of these pairs add to 3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 3\r
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First Number	Second Number	Sum
1	-28	1+(-28)=-27
2	-14	2+(-14)=-12
4	-7	4+(-7)=-3
-1	28	-1+28=27
-2	14	-2+14=12
-4	7	-4+7=3

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -4 and 7 add up to 3 and multiply to -28\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"m%5E2%2B3m-28\"$ , replace $\"3m\"$ with $\"-4m%2B7m\"$ (notice $\"-4m%2B7m\"$ adds up to $\"3m\"$ . So it is equivalent to $\"3m\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"m%5E2%2Bhighlight%28-4m%2B7m%29%2B-28\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"m%5E2-4m%2B7m-28\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%28m%5E2-4m%29%2B%287m-28%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"m%28m-4%29%2B7%28m-4%29\"$ Factor out the GCF of $\"m\"$ out of the first group. Factor out the GCF of $\"7\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28m%2B7%29%28m-4%29\"$ Since we have a common term of $\"m-4\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"m%5E2-4m%2B7m-28\"$ factors to $\"%28m%2B7%29%28m-4%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"m%5E2%2B3m-28\"$ factors to $\"%28m%2B7%29%28m-4%29\"$ (since $\"m%5E2%2B3m-28\"$ is equivalent to $\"m%5E2-4m%2B7m-28\"$ )\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"m%5E2%2B3m-28\"$ factors to $\"%28m%2B7%29%28m-4%29\"$ \r
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