document.write( "Question 634761: I am having difficulty factoring a problem. 49m^2-42m+9 Any help would be appreciated
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Algebra.Com's Answer #399879 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"49m%5E2-42m%2B9\"$ , we can see that the first coefficient is $\"49\"$ , the second coefficient is $\"-42\"$ , and the last term is $\"9\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"49\"$ by the last term $\"9\"$ to get $\"%2849%29%289%29=441\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"441\"$ (the previous product) and add to the second coefficient $\"-42\"$ ?\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 $\"441\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"441\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,3,7,9,21,49,63,147,441\r
\n" ); document.write( "\n" ); document.write( "-1,-3,-7,-9,-21,-49,-63,-147,-441\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 $\"441\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*441 = 441
\n" ); document.write( "3*147 = 441
\n" ); document.write( "7*63 = 441
\n" ); document.write( "9*49 = 441
\n" ); document.write( "21*21 = 441
\n" ); document.write( "(-1)*(-441) = 441
\n" ); document.write( "(-3)*(-147) = 441
\n" ); document.write( "(-7)*(-63) = 441
\n" ); document.write( "(-9)*(-49) = 441
\n" ); document.write( "(-21)*(-21) = 441\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 $\"-42\"$ :\r
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First Number	Second Number	Sum
1	441	1+441=442
3	147	3+147=150
7	63	7+63=70
9	49	9+49=58
21	21	21+21=42
-1	-441	-1+(-441)=-442
-3	-147	-3+(-147)=-150
-7	-63	-7+(-63)=-70
-9	-49	-9+(-49)=-58
-21	-21	-21+(-21)=-42

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-21\"$ and $\"-21\"$ add to $\"-42\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-21\"$ and $\"-21\"$ both multiply to $\"441\"$ and add to $\"-42\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-42m\"$ with $\"-21m-21m\"$ . Remember, $\"-21\"$ and $\"-21\"$ add to $\"-42\"$ . So this shows us that $\"-21m-21m=-42m\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"49m%5E2%2Bhighlight%28-21m-21m%29%2B9\"$ Replace the second term $\"-42m\"$ with $\"-21m-21m\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%2849m%5E2-21m%29%2B%28-21m%2B9%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"7m%287m-3%29%2B%28-21m%2B9%29\"$ Factor out the GCF $\"7m\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"7m%287m-3%29-3%287m-3%29\"$ 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( " $\"%287m-3%29%287m-3%29\"$ Combine like terms. Or factor out the common term $\"7m-3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"%287m-3%29%5E2\"$ Condense the terms.\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"49m%5E2-42m%2B9\"$ factors to $\"%287m-3%29%5E2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"49m%5E2-42m%2B9=%287m-3%29%5E2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%287m-3%29%5E2\"$ to get $\"49m%5E2-42m%2B9\"$ or by graphing the original expression and the answer (the two graphs should be identical).\r
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\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r
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