document.write( "Question 156996: X^2-x-20=? \n" ); document.write( "

Algebra.Com's Answer #115756 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"x%5E2-x-20\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"-1\"$ , and the last term is $\"-20\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"1\"$ by the last term $\"-20\"$ to get $\"%281%29%28-20%29=-20\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-20\"$ (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 $\"-20\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-20\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,4,5,10,20\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-5,-10,-20\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 $\"-20\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-20)
\n" ); document.write( "2*(-10)
\n" ); document.write( "4*(-5)
\n" ); document.write( "(-1)*(20)
\n" ); document.write( "(-2)*(10)
\n" ); document.write( "(-4)*(5)\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	-20	1+(-20)=-19
2	-10	2+(-10)=-8
4	-5	4+(-5)=-1
-1	20	-1+20=19
-2	10	-2+10=8
-4	5	-4+5=1

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"4\"$ and $\"-5\"$ add to $\"-1\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"4\"$ and $\"-5\"$ both multiply to $\"-20\"$ and add to $\"-1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-1x\"$ with $\"4x-5x\"$ . Remember, $\"4\"$ and $\"-5\"$ add to $\"-1\"$ . So this shows us that $\"4x-5x=-1x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bhighlight%284x-5x%29-20\"$ Replace the second term $\"-1x\"$ with $\"4x-5x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2B4x%29%2B%28-5x-20%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x%2B4%29%2B%28-5x-20%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x%2B4%29-5%28x%2B4%29\"$ Factor out $\"5\"$ 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( " $\"%28x-5%29%28x%2B4%29\"$ Combine like terms. Or factor out the common term $\"x%2B4\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E2-x-20\"$ factors to $\"%28x-5%29%28x%2B4%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"x%5E2-x-20=%28x-5%29%28x%2B4%29\"$ .\r
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