document.write( "Question 407530: x^2-12x+20\r
\n" ); document.write( "\n" ); document.write( "It's asking me to factor this\r
\n" ); document.write( "\n" ); document.write( "and that is x squared minus 12x plus 20 \n" ); document.write( "

Algebra.Com's Answer #287289 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 $\"1x%5E2-12x%2B20\"$ we can see that the first term is $\"1x%5E2\"$ and the last term is $\"20\"$ where the coefficients are 1 and 20 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient 20 to get 20. Now what two numbers multiply to 20 and add to the middle coefficient -12? Let's list all of the factors of 20:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 20:\r
\n" ); document.write( "\n" ); document.write( "1,2,4,5,10,20\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-5,-10,-20 ...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 20\r
\n" ); document.write( "\n" ); document.write( "1*20\r
\n" ); document.write( "\n" ); document.write( "2*10\r
\n" ); document.write( "\n" ); document.write( "4*5\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-20)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(-10)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(-5)\r
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\n" ); document.write( "\n" ); document.write( "note: remember two negative numbers multiplied together make a positive number\r
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\n" ); document.write( "\n" ); document.write( "Now which of these pairs add to -12? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -12\r
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First Number	Second Number	Sum
1	20	1+20=21
2	10	2+10=12
4	5	4+5=9
-1	-20	-1+(-20)=-21
-2	-10	-2+(-10)=-12
-4	-5	-4+(-5)=-9

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -2 and -10 add up to -12 and multiply to 20\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"1x%5E2-12x%2B20\"$ , replace $\"-12x\"$ with $\"-2x%2B-10x\"$ (notice $\"-2x%2B-10x\"$ adds up to $\"-12x\"$ . So it is equivalent to $\"-12x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"1x%5E2%2Bhighlight%28-2x%2B-10x%29%2B20\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"1x%5E2-2x-10x%2B20\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%281x%5E2-2x%29%2B%28-10x%2B20%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x-2%29-10%28x-2%29\"$ Factor out the GCF of $\"x\"$ out of the first group. Factor out the GCF of $\"-10\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-10%29%28x-2%29\"$ Since we have a common term of $\"x-2\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"1x%5E2-2x-10x%2B20\"$ factors to $\"%28x-10%29%28x-2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"1x%5E2-12x%2B20\"$ factors to $\"%28x-10%29%28x-2%29\"$ (since $\"1x%5E2-12x%2B20\"$ is equivalent to $\"1x%5E2-2x-10x%2B20\"$ )\r
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\n" ); document.write( "\n" ); document.write( " Answer:\r
\n" ); document.write( "\n" ); document.write( "So $\"x%5E2-12x%2B20\"$ factors to $\"%28x-10%29%28x-2%29\"$ \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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