document.write( "Question 351365: How do you factor 2y^2-15y+12? \n" ); document.write( "

Algebra.Com's Answer #251071 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"2y%5E2-15y%2B12\"$ , we can see that the first coefficient is $\"2\"$ , the second coefficient is $\"-15\"$ , and the last term is $\"12\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"2\"$ by the last term $\"12\"$ to get $\"%282%29%2812%29=24\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"24\"$ (the previous product) and add to the second coefficient $\"-15\"$ ?\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 $\"24\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"24\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,8,12,24\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-8,-12,-24\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 $\"24\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*24 = 24
\n" ); document.write( "2*12 = 24
\n" ); document.write( "3*8 = 24
\n" ); document.write( "4*6 = 24
\n" ); document.write( "(-1)*(-24) = 24
\n" ); document.write( "(-2)*(-12) = 24
\n" ); document.write( "(-3)*(-8) = 24
\n" ); document.write( "(-4)*(-6) = 24\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 $\"-15\"$ :\r
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First Number	Second Number	Sum
1	24	1+24=25
2	12	2+12=14
3	8	3+8=11
4	6	4+6=10
-1	-24	-1+(-24)=-25
-2	-12	-2+(-12)=-14
-3	-8	-3+(-8)=-11
-4	-6	-4+(-6)=-10

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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 $\"-15\"$ . So $\"2y%5E2-15y%2B12\"$ 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 $\"2y%5E2-15y%2B12\"$ doesn't factor at all (over the rational numbers).\r
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\n" ); document.write( "\n" ); document.write( "So $\"2y%5E2-15y%2B12\"$ 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, feel free to check out my tutoring website\r
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\n" ); document.write( "\n" ); document.write( "Jim \n" ); document.write( "

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