document.write( "Question 116761This question is from textbook Intermediate Algebra
\n" ); document.write( ": please help me solve this equation. \"n%5E2-36n%2B320\" \n" ); document.write( "
Algebra.Com's Answer #84904 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
Do you want to factor this?\r
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\n" ); document.write( "\n" ); document.write( "Looking at \"n%5E2-36n%2B320\" we can see that the first term is \"n%5E2\" and the last term is \"320\" where the coefficients are 1 and 320 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient 320 to get 320. Now what two numbers multiply to 320 and add to the middle coefficient -36? Let's list all of the factors of 320:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 320:\r
\n" ); document.write( "\n" ); document.write( "1,2,4,5,8,10,16,20,32,40,64,80,160,320\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-5,-8,-10,-16,-20,-32,-40,-64,-80,-160,-320 ...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 320\r
\n" ); document.write( "\n" ); document.write( "1*320\r
\n" ); document.write( "\n" ); document.write( "2*160\r
\n" ); document.write( "\n" ); document.write( "4*80\r
\n" ); document.write( "\n" ); document.write( "5*64\r
\n" ); document.write( "\n" ); document.write( "8*40\r
\n" ); document.write( "\n" ); document.write( "10*32\r
\n" ); document.write( "\n" ); document.write( "16*20\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-320)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(-160)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(-80)\r
\n" ); document.write( "\n" ); document.write( "(-5)*(-64)\r
\n" ); document.write( "\n" ); document.write( "(-8)*(-40)\r
\n" ); document.write( "\n" ); document.write( "(-10)*(-32)\r
\n" ); document.write( "\n" ); document.write( "(-16)*(-20)\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 -36? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -36\r
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First NumberSecond NumberSum
13201+320=321
21602+160=162
4804+80=84
5645+64=69
8408+40=48
103210+32=42
162016+20=36
-1-320-1+(-320)=-321
-2-160-2+(-160)=-162
-4-80-4+(-80)=-84
-5-64-5+(-64)=-69
-8-40-8+(-40)=-48
-10-32-10+(-32)=-42
-16-20-16+(-20)=-36
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\n" ); document.write( "\n" ); document.write( "From this list we can see that -16 and -20 add up to -36 and multiply to 320\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression \"n%5E2-36n%2B320\", replace \"-36n\" with \"-16n%2B-20n\" (notice \"-16n%2B-20n\" adds up to \"-36n\". So it is equivalent to \"-36n\")\r
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\n" ); document.write( "\n" ); document.write( "\"n%5E2%2Bhighlight%28-16n%2B-20n%29%2B320\"\r
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\n" ); document.write( "\n" ); document.write( "Now let's factor \"n%5E2-16n-20n%2B320\" by grouping:\r
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\n" ); document.write( "\n" ); document.write( "\"%28n%5E2-16n%29%2B%28-20n%2B320%29\" Group like terms\r
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\n" ); document.write( "\n" ); document.write( "\"n%28n-16%29-20%28n-16%29\" Factor out the GCF of \"n\" out of the first group. Factor out the GCF of \"-20\" out of the second group\r
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\n" ); document.write( "\n" ); document.write( "\"%28n-20%29%28n-16%29\" Since we have a common term of \"n-16\", we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So \"n%5E2-16n-20n%2B320\" factors to \"%28n-20%29%28n-16%29\"\r
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\n" ); document.write( "\n" ); document.write( "So this also means that \"n%5E2-36n%2B320\" factors to \"%28n-20%29%28n-16%29\" (since \"n%5E2-36n%2B320\" is equivalent to \"n%5E2-16n-20n%2B320\")\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So \"n%5E2-36n%2B320\" factors to \"%28n-20%29%28n-16%29\"
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