document.write( "Question 7131: I am trying to learn, with great difficulty, how to factor this type of problem... 2a^2-2ab-24b^2 ... I have tried factoring out the 2, but I don't know how to go any further with this problem. How do I find the factors of 12 if there is no factor for the prceding term? Thank you so much for your help. \n" ); document.write( "

Algebra.Com's Answer #3943 by glabow(165) $\"\"$ $\"About$

You can put this solution on YOUR website!
This is one of those things that have two approaches. One is art and the other is science. In this case, the art way is easier.
\n" ); document.write( "The polynomial
\n" ); document.write( " $\"2a%5E2+-+2ab-24b%5E2%29\"$ has an obvious factor, 2.
\n" ); document.write( " $\"2%28a%5E2+-ab+-+12b%5E2%29\"$ must be factored into binomials where
\n" ); document.write( "the $\"a%5E2\"$ term comes from a times a
\n" ); document.write( "the $\"-12b%5E2\"$ term comes from mb times nb, where m times n = -12
\n" ); document.write( "the $\"-ab\"$ term comes from a times mb plus a time nb, where m plus n = -1\r
\n" ); document.write( "\n" ); document.write( "The numbers -4 and 3 satisfy the requirements: -4 times 3 = -12, and -4 plus 3 = -1.
\n" ); document.write( "So the factors are $\"%28a+-4b%29+%28a+%2B+3b%29+=+a%5E2+-ab+-12b%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "The orginal polynomial is $\"2+%28a-4b%29%28a%2B3b%29\"$
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