document.write( "Question 195604: Factor: 2x^2+x-6 \n" ); document.write( "

Algebra.Com's Answer #146694 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at $\"2x%5E2%2Bx-6\"$ we can see that the first term is $\"2x%5E2\"$ and the last term is $\"-6\"$ where the coefficients are 2 and -6 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 2 and the last coefficient -6 to get -12. Now what two numbers multiply to -12 and add to the middle coefficient 1? Let's list all of the factors of -12:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -12:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,12\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-12 ...List the negative factors as well. 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 -12\r
\n" ); document.write( "\n" ); document.write( "(1)*(-12)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-6)\r
\n" ); document.write( "\n" ); document.write( "(3)*(-4)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(12)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(6)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(4)\r
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\n" ); document.write( "\n" ); document.write( "note: remember, the product of a negative and a positive number is a negative number\r
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\n" ); document.write( "\n" ); document.write( "Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1\r
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First Number	Second Number	Sum
1	-12	1+(-12)=-11
2	-6	2+(-6)=-4
3	-4	3+(-4)=-1
-1	12	-1+12=11
-2	6	-2+6=4
-3	4	-3+4=1

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -3 and 4 add up to 1 and multiply to -12\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"2x%5E2%2Bx-6\"$ , replace $\"x\"$ with $\"-3x%2B4x\"$ (notice $\"-3x%2B4x\"$ adds up to $\"x\"$ . So it is equivalent to $\"x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"2x%5E2%2Bhighlight%28-3x%2B4x%29-6\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"2x%5E2-3x%2B4x-6\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%282x%5E2-3x%29%2B%284x-6%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%282x-3%29%2B2%282x-3%29\"$ Factor out the GCF of $\"x\"$ out of the first group. Factor out the GCF of $\"2\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B2%29%282x-3%29\"$ Since we have a common term of $\"2x-3\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"2x%5E2-3x%2B4x-6\"$ factors to $\"%28x%2B2%29%282x-3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"2x%5E2%2Bx-6\"$ factors to $\"%28x%2B2%29%282x-3%29\"$ (since $\"2x%5E2%2Bx-6\"$ is equivalent to $\"2x%5E2-3x%2B4x-6\"$ )\r
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\n" ); document.write( "\n" ); document.write( " Answer:\r
\n" ); document.write( "\n" ); document.write( "So $\"2x%5E2%2Bx-6\"$ factors to $\"%28x%2B2%29%282x-3%29\"$
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