document.write( "Question 616008: Factor. Remember to use the largest common factor and to check by multiplying. Factor out a negative factor if the first coefficient is negative.
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Algebra.Com's Answer #387445 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"-10t%5E5%2B15t%5E4%2B9t%5E3\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"-1t%5E3%2810t%5E2-15t-9%29\"$ Factor out the GCF $\"-1t%5E3\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now let's try to factor the inner expression $\"10t%5E2-15t-9\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"10t%5E2-15t-9\"$ , we can see that the first coefficient is $\"10\"$ , the second coefficient is $\"-15\"$ , and the last term is $\"-9\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"10\"$ by the last term $\"-9\"$ to get $\"%2810%29%28-9%29=-90\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-90\"$ (the previous product) and add to the second coefficient $\"-15\"$ ?\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 $\"-90\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-90\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,5,6,9,10,15,18,30,45,90\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-5,-6,-9,-10,-15,-18,-30,-45,-90\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 $\"-90\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-90) = -90
\n" ); document.write( "2*(-45) = -90
\n" ); document.write( "3*(-30) = -90
\n" ); document.write( "5*(-18) = -90
\n" ); document.write( "6*(-15) = -90
\n" ); document.write( "9*(-10) = -90
\n" ); document.write( "(-1)*(90) = -90
\n" ); document.write( "(-2)*(45) = -90
\n" ); document.write( "(-3)*(30) = -90
\n" ); document.write( "(-5)*(18) = -90
\n" ); document.write( "(-6)*(15) = -90
\n" ); document.write( "(-9)*(10) = -90\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 $\"-15\"$ :\r
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First Number	Second Number	Sum
1	-90	1+(-90)=-89
2	-45	2+(-45)=-43
3	-30	3+(-30)=-27
5	-18	5+(-18)=-13
6	-15	6+(-15)=-9
9	-10	9+(-10)=-1
-1	90	-1+90=89
-2	45	-2+45=43
-3	30	-3+30=27
-5	18	-5+18=13
-6	15	-6+15=9
-9	10	-9+10=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 $\"-15\"$ . So $\"10t%5E2-15t-9\"$ 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 $\"-10t%5E5%2B15t%5E4%2B9t%5E3\"$ simply factors to $\"-t%5E3%2810t%5E2-15t-9%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"-10t%5E5%2B15t%5E4%2B9t%5E3=-t%5E3%2810t%5E2-15t-9%29\"$ .
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