document.write( "Question 725322: 6x^2+18x-600
\n" ); document.write( "Factor, if possible. Be sure to factor completely. Always factor out the greatest commone factor first, if one exist.
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Algebra.Com's Answer #444094 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"6x%5E2%2B18x-600\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"6%28x%5E2%2B3x-100%29\"$ Factor out the GCF $\"6\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now let's try to factor the inner expression $\"x%5E2%2B3x-100\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"x%5E2%2B3x-100\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"3\"$ , and the last term is $\"-100\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"1\"$ by the last term $\"-100\"$ to get $\"%281%29%28-100%29=-100\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-100\"$ (the previous product) and add to the second coefficient $\"3\"$ ?\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 $\"-100\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-100\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,4,5,10,20,25,50,100\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-5,-10,-20,-25,-50,-100\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 $\"-100\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-100) = -100
\n" ); document.write( "2*(-50) = -100
\n" ); document.write( "4*(-25) = -100
\n" ); document.write( "5*(-20) = -100
\n" ); document.write( "10*(-10) = -100
\n" ); document.write( "(-1)*(100) = -100
\n" ); document.write( "(-2)*(50) = -100
\n" ); document.write( "(-4)*(25) = -100
\n" ); document.write( "(-5)*(20) = -100
\n" ); document.write( "(-10)*(10) = -100\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 $\"3\"$ :\r
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First Number	Second Number	Sum
1	-100	1+(-100)=-99
2	-50	2+(-50)=-48
4	-25	4+(-25)=-21
5	-20	5+(-20)=-15
10	-10	10+(-10)=0
-1	100	-1+100=99
-2	50	-2+50=48
-4	25	-4+25=21
-5	20	-5+20=15
-10	10	-10+10=0

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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 $\"3\"$ . So $\"x%5E2%2B3x-100\"$ 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 $\"6x%5E2%2B18x-600\"$ simply factors to $\"6%28x%5E2%2B3x-100%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"6x%5E2%2B18x-600=6%28x%5E2%2B3x-100%29\"$ .
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