document.write( "Question 379889: Hi, can you completely factor this problem? 5x^2-4x+12 I tried everything, but nothing seems to work. Thanks. \n" ); document.write( "

Algebra.Com's Answer #269680 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Looking at the expression $\"5x%5E2-4x%2B12\"$ , we can see that the first coefficient is $\"5\"$ , the second coefficient is $\"-4\"$ , and the last term is $\"12\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"5\"$ by the last term $\"12\"$ to get $\"%285%29%2812%29=60\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"60\"$ (the previous product) and add to the second coefficient $\"-4\"$ ?\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 $\"60\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"60\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,5,6,10,12,15,20,30,60\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60\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 $\"60\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*60 = 60
\n" ); document.write( "2*30 = 60
\n" ); document.write( "3*20 = 60
\n" ); document.write( "4*15 = 60
\n" ); document.write( "5*12 = 60
\n" ); document.write( "6*10 = 60
\n" ); document.write( "(-1)*(-60) = 60
\n" ); document.write( "(-2)*(-30) = 60
\n" ); document.write( "(-3)*(-20) = 60
\n" ); document.write( "(-4)*(-15) = 60
\n" ); document.write( "(-5)*(-12) = 60
\n" ); document.write( "(-6)*(-10) = 60\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 $\"-4\"$ :\r
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First Number	Second Number	Sum
1	60	1+60=61
2	30	2+30=32
3	20	3+20=23
4	15	4+15=19
5	12	5+12=17
6	10	6+10=16
-1	-60	-1+(-60)=-61
-2	-30	-2+(-30)=-32
-3	-20	-3+(-20)=-23
-4	-15	-4+(-15)=-19
-5	-12	-5+(-12)=-17
-6	-10	-6+(-10)=-16

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