document.write( "Question 199608This question is from textbook Beginning and Intermediate Algebra
\n" ); document.write( ": Find any variables for which the rational expression is undefined.
\n" ); document.write( "5m + 2
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\n" ); document.write( "m(squared) + m - 6\r
\n" ); document.write( "\n" ); document.write( "I tried to set the denominator equal to 0, then factor, but I am stuck on the factoring. Any help is appreciated. \n" ); document.write( "

Algebra.Com's Answer #150001 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"m%5E2%2Bm-6\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"1\"$ , and the last term is $\"-6\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"1\"$ by the last term $\"-6\"$ to get $\"%281%29%28-6%29=-6\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-6\"$ (the previous product) and add to the second coefficient $\"1\"$ ?\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 $\"-6\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-6\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,6\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-6\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 $\"-6\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-6)
\n" ); document.write( "2*(-3)
\n" ); document.write( "(-1)*(6)
\n" ); document.write( "(-2)*(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 $\"1\"$ :\r
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First Number	Second Number	Sum
1	-6	1+(-6)=-5
2	-3	2+(-3)=-1
-1	6	-1+6=5
-2	3	-2+3=1

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-2\"$ and $\"3\"$ add to $\"1\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-2\"$ and $\"3\"$ both multiply to $\"-6\"$ and add to $\"1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"1m\"$ with $\"-2m%2B3m\"$ . Remember, $\"-2\"$ and $\"3\"$ add to $\"1\"$ . So this shows us that $\"-2m%2B3m=1m\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"m%5E2%2Bhighlight%28-2m%2B3m%29-6\"$ Replace the second term $\"1m\"$ with $\"-2m%2B3m\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%28m%5E2-2m%29%2B%283m-6%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"m%28m-2%29%2B%283m-6%29\"$ Factor out the GCF $\"m\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"m%28m-2%29%2B3%28m-2%29\"$ 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( " $\"%28m%2B3%29%28m-2%29\"$ Combine like terms. Or factor out the common term $\"m-2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"m%5E2%2Bm-6\"$ factors to $\"%28m%2B3%29%28m-2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "From here, you can use the factored form to solve for \"m\" \n" ); document.write( "

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