document.write( "Question 607737: can you explain to me how i would solve this i am so confused.
\n" ); document.write( "Factor completely: -12x3y5 - 9x2y2 + 12xy3?
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Algebra.Com's Answer #382883 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " $\"-12x%5E3y%5E5-9x%5E2y%5E2%2B12xy%5E3\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"-3xy%5E2%284x%5E2y%5E3%2B3x-4y%29\"$ Factor out the GCF $\"-3xy%5E2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now let's try to factor the inner expression $\"4x%5E2y%5E3%2B3x-4y\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"4x%5E2y%5E3%2B3x-4y\"$ , we can see that the first coefficient is $\"4\"$ , the second coefficient is $\"3\"$ , and the last coefficient is $\"-4\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"4\"$ by the last coefficient $\"-4\"$ to get $\"%284%29%28-4%29=-16\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-16\"$ (the previous product) and add to the second coefficient $\"3\"$ ?\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 $\"-16\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-16\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,4,8,16\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-8,-16\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 $\"-16\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-16) = -16
\n" ); document.write( "2*(-8) = -16
\n" ); document.write( "4*(-4) = -16
\n" ); document.write( "(-1)*(16) = -16
\n" ); document.write( "(-2)*(8) = -16
\n" ); document.write( "(-4)*(4) = -16\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 $\"3\"$ :\r
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First Number	Second Number	Sum
1	-16	1+(-16)=-15
2	-8	2+(-8)=-6
4	-4	4+(-4)=0
-1	16	-1+16=15
-2	8	-2+8=6
-4	4	-4+4=0

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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 $\"3\"$ . So $\"4x%5E2y%5E3%2B3x-4y\"$ 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 $\"-12x%5E3y%5E5-9x%5E2y%5E2%2B12xy%5E3\"$ simply factors to $\"-3xy%5E2%284x%5E2y%5E3%2B3x-4y%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"-12x%5E3y%5E5-9x%5E2y%5E2%2B12xy%5E3=-3xy%5E2%284x%5E2y%5E3%2B3x-4y%29\"$ .\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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\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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