document.write( "Question 127884: 24x+2x-12 \n" ); document.write( "

Algebra.Com's Answer #93662 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Do you mean $\"24x%5E2%2B2x-12\"$ ? Do you want to factor?\r
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\n" ); document.write( "\n" ); document.write( " $\"24x%5E2%2B2x-12\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"2%2812x%5E2%2Bx-6%29\"$ Factor out the GCF $\"2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"12x%5E2%2Bx-6\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"12x%5E2%2B1x-6\"$ we can see that the first term is $\"12x%5E2\"$ and the last term is $\"-6\"$ where the coefficients are 12 and -6 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 12 and the last coefficient -6 to get -72. Now what two numbers multiply to -72 and add to the middle coefficient 1? Let's list all of the factors of -72:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -72:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,8,9,12,18,24,36,72\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-8,-9,-12,-18,-24,-36,-72 ...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 -72\r
\n" ); document.write( "\n" ); document.write( "(1)*(-72)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-36)\r
\n" ); document.write( "\n" ); document.write( "(3)*(-24)\r
\n" ); document.write( "\n" ); document.write( "(4)*(-18)\r
\n" ); document.write( "\n" ); document.write( "(6)*(-12)\r
\n" ); document.write( "\n" ); document.write( "(8)*(-9)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(72)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(36)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(24)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(18)\r
\n" ); document.write( "\n" ); document.write( "(-6)*(12)\r
\n" ); document.write( "\n" ); document.write( "(-8)*(9)\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	-72	1+(-72)=-71
2	-36	2+(-36)=-34
3	-24	3+(-24)=-21
4	-18	4+(-18)=-14
6	-12	6+(-12)=-6
8	-9	8+(-9)=-1
-1	72	-1+72=71
-2	36	-2+36=34
-3	24	-3+24=21
-4	18	-4+18=14
-6	12	-6+12=6
-8	9	-8+9=1

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -8 and 9 add up to 1 and multiply to -72\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"12x%5E2%2B1x-6\"$ , replace $\"1x\"$ with $\"-8x%2B9x\"$ (notice $\"-8x%2B9x\"$ adds up to $\"1x\"$ . So it is equivalent to $\"1x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"12x%5E2%2Bhighlight%28-8x%2B9x%29%2B-6\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"12x%5E2-8x%2B9x-6\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%2812x%5E2-8x%29%2B%289x-6%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"4x%283x-2%29%2B3%283x-2%29\"$ Factor out the GCF of $\"4x\"$ out of the first group. Factor out the GCF of $\"3\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%284x%2B3%29%283x-2%29\"$ Since we have a common term of $\"3x-2\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"12x%5E2-8x%2B9x-6\"$ factors to $\"%284x%2B3%29%283x-2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"12x%5E2%2B1x-6\"$ factors to $\"%284x%2B3%29%283x-2%29\"$ (since $\"12x%5E2%2B1x-6\"$ is equivalent to $\"12x%5E2-8x%2B9x-6\"$ )\r
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\n" ); document.write( "\n" ); document.write( "So our expression goes from $\"2%2812x%5E2%2Bx-6%29\"$ and factors further to $\"2%284x%2B3%29%283x-2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"24x%5E2%2B2x-12\"$ factors to $\"2%284x%2B3%29%283x-2%29\"$ \r
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