document.write( "Question 620953: x2 – 5x – 6 \n" ); document.write( "

Algebra.Com's Answer #390473 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"x%5E2-5x-6\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"-5\"$ , and the last term is $\"-6\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"1\"$ by the last term $\"-6\"$ to get $\"%281%29%28-6%29=-6\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-6\"$ (the previous product) and add to the second coefficient $\"-5\"$ ?\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 $\"-6\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-6\"$ :\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-6\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 $\"-6\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-6) = -6
\n" ); document.write( "2*(-3) = -6
\n" ); document.write( "(-1)*(6) = -6
\n" ); document.write( "(-2)*(3) = -6\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 $\"-5\"$ :\r
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First Number	Second Number	Sum
1	-6	1+(-6)=-5
2	-3	2+(-3)=-1
-1	6	-1+6=5
-2	3	-2+3=1

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"1\"$ and $\"-6\"$ add to $\"-5\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"1\"$ and $\"-6\"$ both multiply to $\"-6\"$ and add to $\"-5\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-5x\"$ with $\"x-6x\"$ . Remember, $\"1\"$ and $\"-6\"$ add to $\"-5\"$ . So this shows us that $\"x-6x=-5x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bhighlight%28x-6x%29-6\"$ Replace the second term $\"-5x\"$ with $\"x-6x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2Bx%29%2B%28-6x-6%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x%2B1%29%2B%28-6x-6%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x%2B1%29-6%28x%2B1%29\"$ Factor out $\"6\"$ 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( " $\"%28x-6%29%28x%2B1%29\"$ Combine like terms. Or factor out the common term $\"x%2B1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E2-5x-6\"$ factors to $\"%28x-6%29%28x%2B1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"x%5E2-5x-6=%28x-6%29%28x%2B1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%28x-6%29%28x%2B1%29\"$ to get $\"x%5E2-5x-6\"$ or by graphing the original expression and the answer (the two graphs should be identical).
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