document.write( "Question 117350: Help Factor Completely:
\n" ); document.write( "24x^2 + 10x – 4\r
\n" ); document.write( "\n" ); document.write( "Could you please list it in step by step directions? For some reason, this is a concept I cannot grasp. \r
\n" ); document.write( "\n" ); document.write( "Thank you in advance!
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Algebra.Com's Answer #85368 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"24x%5E2%2B10x-4\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"2%2812x%5E2%2B5x-2%29\"$ Factor out the GCF $\"2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"12x%5E2%2B5x-2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"12x%5E2%2B5x-2\"$ we can see that the first term is $\"12x%5E2\"$ and the last term is $\"-2\"$ where the coefficients are 12 and -2 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 12 and the last coefficient -2 to get -24. Now what two numbers multiply to -24 and add to the middle coefficient 5? Let's list all of the factors of -24:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -24:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,8,12,24\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-8,-12,-24 ...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 -24\r
\n" ); document.write( "\n" ); document.write( "(1)*(-24)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-12)\r
\n" ); document.write( "\n" ); document.write( "(3)*(-8)\r
\n" ); document.write( "\n" ); document.write( "(4)*(-6)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(24)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(12)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(8)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(6)\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 5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 5\r
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First Number	Second Number	Sum
1	-24	1+(-24)=-23
2	-12	2+(-12)=-10
3	-8	3+(-8)=-5
4	-6	4+(-6)=-2
-1	24	-1+24=23
-2	12	-2+12=10
-3	8	-3+8=5
-4	6	-4+6=2

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -3 and 8 add up to 5 and multiply to -24\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"12x%5E2%2B5x-2\"$ , replace $\"5x\"$ with $\"-3x%2B8x\"$ (notice $\"-3x%2B8x\"$ adds up to $\"5x\"$ . So it is equivalent to $\"5x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"12x%5E2%2Bhighlight%28-3x%2B8x%29%2B-2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"12x%5E2-3x%2B8x-2\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%2812x%5E2-3x%29%2B%288x-2%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"3x%284x-1%29%2B2%284x-1%29\"$ Factor out the GCF of $\"3x\"$ 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( " $\"%283x%2B2%29%284x-1%29\"$ Since we have a common term of $\"4x-1\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"12x%5E2%2B5x-2\"$ factors to $\"%283x%2B2%29%284x-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"2%283x%2B2%29%284x-1%29\"$ Reintroduce the GCF\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"24x%5E2%2B10x-4\"$ factors to $\"2%283x%2B2%29%284x-1%29\"$ \n" ); document.write( "

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