document.write( "Question 419968: How do I solve this problem... 5n^2-26n+21 \n" ); document.write( "

Algebra.Com's Answer #293546 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'm assuming you want to factor this.\r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"5n%5E2-26n%2B21\"$ we can see that the first term is $\"5n%5E2\"$ and the last term is $\"21\"$ where the coefficients are 5 and 21 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 5 and the last coefficient 21 to get 105. Now what two numbers multiply to 105 and add to the middle coefficient -26? Let's list all of the factors of 105:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 105:\r
\n" ); document.write( "\n" ); document.write( "1,3,5,7,15,21,35,105\r
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\n" ); document.write( "\n" ); document.write( "-1,-3,-5,-7,-15,-21,-35,-105 ...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 105\r
\n" ); document.write( "\n" ); document.write( "1*105\r
\n" ); document.write( "\n" ); document.write( "3*35\r
\n" ); document.write( "\n" ); document.write( "5*21\r
\n" ); document.write( "\n" ); document.write( "7*15\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-105)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(-35)\r
\n" ); document.write( "\n" ); document.write( "(-5)*(-21)\r
\n" ); document.write( "\n" ); document.write( "(-7)*(-15)\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 -26? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -26\r
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First Number	Second Number	Sum
1	105	1+105=106
3	35	3+35=38
5	21	5+21=26
7	15	7+15=22
-1	-105	-1+(-105)=-106
-3	-35	-3+(-35)=-38
-5	-21	-5+(-21)=-26
-7	-15	-7+(-15)=-22

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -5 and -21 add up to -26 and multiply to 105\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"5n%5E2-26n%2B21\"$ , replace $\"-26n\"$ with $\"-5n%2B-21n\"$ (notice $\"-5n%2B-21n\"$ adds up to $\"-26n\"$ . So it is equivalent to $\"-26n\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"5n%5E2%2Bhighlight%28-5n%2B-21n%29%2B21\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"5n%5E2-5n-21n%2B21\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%285n%5E2-5n%29%2B%28-21n%2B21%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"5n%28n-1%29-21%28n-1%29\"$ Factor out the GCF of $\"5n\"$ out of the first group. Factor out the GCF of $\"-21\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%285n-21%29%28n-1%29\"$ Since we have a common term of $\"n-1\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"5n%5E2-5n-21n%2B21\"$ factors to $\"%285n-21%29%28n-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"5n%5E2-26n%2B21\"$ factors to $\"%285n-21%29%28n-1%29\"$ (since $\"5n%5E2-26n%2B21\"$ is equivalent to $\"5n%5E2-5n-21n%2B21\"$ )\r
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\n" ); document.write( "\n" ); document.write( " Answer:\r
\n" ); document.write( "\n" ); document.write( "So $\"5n%5E2-26n%2B21\"$ factors to $\"%285n-21%29%28n-1%29\"$ \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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