document.write( "Question 760562: factor 12h^2 -13hj -4j^2 \n" ); document.write( "

Algebra.Com's Answer #462754 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"12h%5E2-13hj-4j%5E2\"$ , we can see that the first coefficient is $\"12\"$ , the second coefficient is $\"-13\"$ , and the last coefficient is $\"-4\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"12\"$ by the last coefficient $\"-4\"$ to get $\"%2812%29%28-4%29=-48\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-48\"$ (the previous product) and add to the second coefficient $\"-13\"$ ?\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 $\"-48\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-48\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,8,12,16,24,48\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-8,-12,-16,-24,-48\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 $\"-48\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-48) = -48
\n" ); document.write( "2*(-24) = -48
\n" ); document.write( "3*(-16) = -48
\n" ); document.write( "4*(-12) = -48
\n" ); document.write( "6*(-8) = -48
\n" ); document.write( "(-1)*(48) = -48
\n" ); document.write( "(-2)*(24) = -48
\n" ); document.write( "(-3)*(16) = -48
\n" ); document.write( "(-4)*(12) = -48
\n" ); document.write( "(-6)*(8) = -48\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 $\"-13\"$ :\r
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First Number	Second Number	Sum
1	-48	1+(-48)=-47
2	-24	2+(-24)=-22
3	-16	3+(-16)=-13
4	-12	4+(-12)=-8
6	-8	6+(-8)=-2
-1	48	-1+48=47
-2	24	-2+24=22
-3	16	-3+16=13
-4	12	-4+12=8
-6	8	-6+8=2

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"3\"$ and $\"-16\"$ add to $\"-13\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"3\"$ and $\"-16\"$ both multiply to $\"-48\"$ and add to $\"-13\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-13hj\"$ with $\"3hj-16hj\"$ . Remember, $\"3\"$ and $\"-16\"$ add to $\"-13\"$ . So this shows us that $\"3hj-16hj=-13hj\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"12h%5E2%2Bhighlight%283hj-16hj%29-4j%5E2\"$ Replace the second term $\"-13hj\"$ with $\"3hj-16hj\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%2812h%5E2%2B3hj%29%2B%28-16hj-4j%5E2%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"3h%284h%2Bj%29%2B%28-16hj-4j%5E2%29\"$ Factor out the GCF $\"3h\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"3h%284h%2Bj%29-4j%284h%2Bj%29\"$ Factor out $\"-4j\"$ from the second group.\r
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\n" ); document.write( "\n" ); document.write( " $\"%283h-4j%29%284h%2Bj%29\"$ Factor out the GCF $\"4h%2Bj\"$ from the entire expression\r
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\n" ); document.write( "\n" ); document.write( "Final Answer: $\"%283h-4j%29%284h%2Bj%29\"$
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