document.write( "Question 656096: how do you factor 3x^2+10x-10 \n" ); document.write( "

Algebra.Com's Answer #409402 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"3x%5E2%2B10x-10\"$ , we can see that the first coefficient is $\"3\"$ , the second coefficient is $\"10\"$ , and the last term is $\"-10\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"3\"$ by the last term $\"-10\"$ to get $\"%283%29%28-10%29=-30\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-30\"$ (the previous product) and add to the second coefficient $\"10\"$ ?\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 $\"-30\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-30\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,5,6,10,15,30\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-5,-6,-10,-15,-30\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 $\"-30\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-30) = -30
\n" ); document.write( "2*(-15) = -30
\n" ); document.write( "3*(-10) = -30
\n" ); document.write( "5*(-6) = -30
\n" ); document.write( "(-1)*(30) = -30
\n" ); document.write( "(-2)*(15) = -30
\n" ); document.write( "(-3)*(10) = -30
\n" ); document.write( "(-5)*(6) = -30\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 $\"10\"$ :\r
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First Number	Second Number	Sum
1	-30	1+(-30)=-29
2	-15	2+(-15)=-13
3	-10	3+(-10)=-7
5	-6	5+(-6)=-1
-1	30	-1+30=29
-2	15	-2+15=13
-3	10	-3+10=7
-5	6	-5+6=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 $\"10\"$ . So $\"3x%5E2%2B10x-10\"$ 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 $\"3x%5E2%2B10x-10\"$ doesn't factor at all (over the rational numbers).\r
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\n" ); document.write( "\n" ); document.write( "So $\"3x%5E2%2B10x-10\"$ is prime.
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