document.write( "Question 540467: How do you factor m^2 + 30m - 96 \n" ); document.write( "

Algebra.Com's Answer #353717 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"m%5E2%2B30m-96\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"30\"$ , and the last term is $\"-96\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"1\"$ by the last term $\"-96\"$ to get $\"%281%29%28-96%29=-96\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-96\"$ (the previous product) and add to the second coefficient $\"30\"$ ?\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 $\"-96\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-96\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,8,12,16,24,32,48,96\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-8,-12,-16,-24,-32,-48,-96\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 $\"-96\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-96) = -96
\n" ); document.write( "2*(-48) = -96
\n" ); document.write( "3*(-32) = -96
\n" ); document.write( "4*(-24) = -96
\n" ); document.write( "6*(-16) = -96
\n" ); document.write( "8*(-12) = -96
\n" ); document.write( "(-1)*(96) = -96
\n" ); document.write( "(-2)*(48) = -96
\n" ); document.write( "(-3)*(32) = -96
\n" ); document.write( "(-4)*(24) = -96
\n" ); document.write( "(-6)*(16) = -96
\n" ); document.write( "(-8)*(12) = -96\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 $\"30\"$ :\r
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First Number	Second Number	Sum
1	-96	1+(-96)=-95
2	-48	2+(-48)=-46
3	-32	3+(-32)=-29
4	-24	4+(-24)=-20
6	-16	6+(-16)=-10
8	-12	8+(-12)=-4
-1	96	-1+96=95
-2	48	-2+48=46
-3	32	-3+32=29
-4	24	-4+24=20
-6	16	-6+16=10
-8	12	-8+12=4

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that there are no pairs of numbers which add to $\"30\"$ . So $\"m%5E2%2B30m-96\"$ cannot be factored.\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"m%5E2%2B30m-96\"$ doesn't factor at all (over the rational numbers).\r
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\n" ); document.write( "\n" ); document.write( "So $\"m%5E2%2B30m-96\"$ is prime.\r
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\n" ); document.write( "\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r
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\n" ); document.write( "\n" ); document.write( "Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you\r
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\n" ); document.write( "\n" ); document.write( "Jim
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