document.write( "Question 405580: I am needing some help with this...\r
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Algebra.Com's Answer #286454 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( " $\"10a%5E2%2B25a-15\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"5%282a%5E2%2B5a-3%29\"$ Factor out the GCF $\"5\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"2a%5E2%2B5a-3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"2a%5E2%2B5a-3\"$ we can see that the first term is $\"2a%5E2\"$ and the last term is $\"-3\"$ where the coefficients are 2 and -3 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 2 and the last coefficient -3 to get -6. Now what two numbers multiply to -6 and add to the middle coefficient 5? Let's list all of the factors of -6:\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
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-6 ...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 -6\r
\n" ); document.write( "\n" ); document.write( "(1)*(-6)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-3)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(6)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(3)\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	-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 this list we can see that -1 and 6 add up to 5 and multiply to -6\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"2a%5E2%2B5a-3\"$ , replace $\"5a\"$ with $\"-a%2B6a\"$ (notice $\"-a%2B6a\"$ adds up to $\"5a\"$ . So it is equivalent to $\"5a\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"2a%5E2%2Bhighlight%28-a%2B6a%29-3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"2a%5E2-a%2B6a-3\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%282a%5E2-a%29%2B%286a-3%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"a%282a-1%29%2B3%282a-1%29\"$ Factor out the GCF of $\"a\"$ 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( " $\"%28a%2B3%29%282a-1%29\"$ Since we have a common term of $\"2a-1\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"2a%5E2-a%2B6a-3\"$ factors to $\"%28a%2B3%29%282a-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"2a%5E2%2B5a-3\"$ factors to $\"%28a%2B3%29%282a-1%29\"$ (since $\"2a%5E2%2B5a-3\"$ is equivalent to $\"2a%5E2-a%2B6a-3\"$ )\r
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\n" ); document.write( "\n" ); document.write( "So our expression goes from $\"5%282a%5E2%2B5a-3%29\"$ and factors further to $\"5%28a%2B3%29%282a-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"10a%5E2%2B25a-15\"$ factors to $\"5%28a%2B3%29%282a-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r
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\n" ); document.write( "\n" ); document.write( "Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you\r
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\n" ); document.write( "\n" ); document.write( "Jim \n" ); document.write( "

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