document.write( "Question 119713: Was I able to factor this correctly?
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Algebra.Com's Answer #87707 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Looking at $\"4x%5E2-15x-25\"$ we can see that the first term is $\"4x%5E2\"$ and the last term is $\"-25\"$ where the coefficients are 4 and -25 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 4 and the last coefficient -25 to get -100. Now what two numbers multiply to -100 and add to the middle coefficient -15? Let's list all of the factors of -100:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -100:\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-5,-10,-20,-25,-50 ...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 -100\r
\n" ); document.write( "\n" ); document.write( "(1)*(-100)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-50)\r
\n" ); document.write( "\n" ); document.write( "(4)*(-25)\r
\n" ); document.write( "\n" ); document.write( "(5)*(-20)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(100)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(50)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(25)\r
\n" ); document.write( "\n" ); document.write( "(-5)*(20)\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 -15? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -15\r
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First Number	Second Number	Sum
1	-100	1+(-100)=-99
2	-50	2+(-50)=-48
4	-25	4+(-25)=-21
5	-20	5+(-20)=-15
-1	100	-1+100=99
-2	50	-2+50=48
-4	25	-4+25=21
-5	20	-5+20=15

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\n" ); document.write( "\n" ); document.write( "From this list we can see that 5 and -20 add up to -15 and multiply to -100\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"4x%5E2-15x-25\"$ , replace $\"-15x\"$ with $\"5x%2B-20x\"$ (notice $\"5x%2B-20x\"$ adds up to $\"-15x\"$ . So it is equivalent to $\"-15x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"4x%5E2%2Bhighlight%285x%2B-20x%29%2B-25\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"4x%5E2%2B5x-20x-25\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%284x%5E2%2B5x%29%2B%28-20x-25%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%284x%2B5%29-5%284x%2B5%29\"$ Factor out the GCF of $\"x\"$ out of the first group. Factor out the GCF of $\"-5\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-5%29%284x%2B5%29\"$ Since we have a common term of $\"4x%2B5\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"4x%5E2%2B5x-20x-25\"$ factors to $\"%28x-5%29%284x%2B5%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"4x%5E2-15x-25\"$ factors to $\"%28x-5%29%284x%2B5%29\"$ (since $\"4x%5E2-15x-25\"$ is equivalent to $\"4x%5E2%2B5x-20x-25\"$ )\r
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\n" ); document.write( "\n" ); document.write( "So $\"4x%5E2-15x-25\"$ factors to $\"%28x-5%29%284x%2B5%29\"$ \r
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