document.write( "Question 660583: -9x^2+81x+180 factor completely \n" ); document.write( "

Algebra.Com's Answer #411260 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"-9x%5E2%2B81x%2B180\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"-9%28x%5E2-9x-20%29\"$ Factor out the GCF $\"-9\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now let's try to factor the inner expression $\"x%5E2-9x-20\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"x%5E2-9x-20\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"-9\"$ , 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 $\"-9\"$ ?\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) = -20
\n" ); document.write( "2*(-10) = -20
\n" ); document.write( "4*(-5) = -20
\n" ); document.write( "(-1)*(20) = -20
\n" ); document.write( "(-2)*(10) = -20
\n" ); document.write( "(-4)*(5) = -20\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 $\"-9\"$ :\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 there are no pairs of numbers which add to $\"-9\"$ . So $\"x%5E2-9x-20\"$ cannot be factored.\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"-9x%5E2%2B81x%2B180\"$ simply factors to $\"-9%28x%5E2-9x-20%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"-9x%5E2%2B81x%2B180=-9%28x%5E2-9x-20%29\"$ .
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