document.write( "Question 203897: please explain to me how you decide which sign (positive/negative)is assigned to each of the factored parts:\r
\n" ); document.write( "\n" ); document.write( "Solve: 3x^2 = 2 - x. My text shows the factor as (3x-2) (x+1)= 0 I thought that when the constant is negative (i.e. 3x^2 + x - 2 = 0), you need a positive & negative sign. You determine which by assigning the sign of the \"b\" constant to the larger absolute value. \n" ); document.write( "

Algebra.Com's Answer #153830 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"3x%5E2+=+2+-+x\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"3x%5E2+%2Bx-2=0\"$ Add \"x\" to both sides. Subtract 2 from both sides.\r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"3x%5E2%2Bx-2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"3x%5E2%2Bx-2\"$ , we can see that the first coefficient is $\"3\"$ , the second coefficient is $\"1\"$ , and the last term is $\"-2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"3\"$ by the last term $\"-2\"$ to get $\"%283%29%28-2%29=-6\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-6\"$ (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 $\"-6\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-6\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,6\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-6\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 $\"-6\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-6)
\n" ); document.write( "2*(-3)
\n" ); document.write( "(-1)*(6)
\n" ); document.write( "(-2)*(3)\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	-6	1+(-6)=-5
2	-3	2+(-3)=-1
-1	6	-1+6=5
-2	3	-2+3=1

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-2\"$ and $\"3\"$ add to $\"1\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-2\"$ and $\"3\"$ both multiply to $\"-6\"$ and add to $\"1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"1x\"$ with $\"-2x%2B3x\"$ . Remember, $\"-2\"$ and $\"3\"$ add to $\"1\"$ . So this shows us that $\"-2x%2B3x=1x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"3x%5E2%2Bhighlight%28-2x%2B3x%29-2\"$ Replace the second term $\"1x\"$ with $\"-2x%2B3x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%283x%5E2-2x%29%2B%283x-2%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%283x-2%29%2B%283x-2%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%283x-2%29%2B1%283x-2%29\"$ Factor out $\"1\"$ 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( " $\"%28x%2B1%29%283x-2%29\"$ Combine like terms. Or factor out the common term $\"3x-2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"3x%5E2%2Bx-2\"$ factors to $\"%28x%2B1%29%283x-2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: the order of the factors does not matter.
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