document.write( "Question 281667: i need help with this problem X squared -X - 12 \n" ); document.write( "

Algebra.Com's Answer #204635 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'm assuming that you want to factor.\r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"x%5E2-x-12\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"-1\"$ , and the last term is $\"-12\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"1\"$ by the last term $\"-12\"$ to get $\"%281%29%28-12%29=-12\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-12\"$ (the previous product) and add to the second coefficient $\"-1\"$ ?\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 $\"-12\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-12\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,12\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-12\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 $\"-12\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-12) = -12
\n" ); document.write( "2*(-6) = -12
\n" ); document.write( "3*(-4) = -12
\n" ); document.write( "(-1)*(12) = -12
\n" ); document.write( "(-2)*(6) = -12
\n" ); document.write( "(-3)*(4) = -12\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 $\"-1\"$ :\r
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First Number	Second Number	Sum
1	-12	1+(-12)=-11
2	-6	2+(-6)=-4
3	-4	3+(-4)=-1
-1	12	-1+12=11
-2	6	-2+6=4
-3	4	-3+4=1

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"3\"$ and $\"-4\"$ add to $\"-1\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"3\"$ and $\"-4\"$ both multiply to $\"-12\"$ and add to $\"-1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-1x\"$ with $\"3x-4x\"$ . Remember, $\"3\"$ and $\"-4\"$ add to $\"-1\"$ . So this shows us that $\"3x-4x=-1x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bhighlight%283x-4x%29-12\"$ Replace the second term $\"-1x\"$ with $\"3x-4x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2B3x%29%2B%28-4x-12%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x%2B3%29%2B%28-4x-12%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x%2B3%29-4%28x%2B3%29\"$ Factor out $\"4\"$ from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-4%29%28x%2B3%29\"$ Combine like terms. Or factor out the common term $\"x%2B3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E2-x-12\"$ factors to $\"%28x-4%29%28x%2B3%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"x%5E2-x-12=%28x-4%29%28x%2B3%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%28x-4%29%28x%2B3%29\"$ to get $\"x%5E2-x-12\"$ or by graphing the original expression and the answer (the two graphs should be identical).
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