document.write( "Question 117558: c^2+19c+60\r
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Algebra.Com's Answer #85543 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at $\"c%5E2%2B19c%2B60\"$ we can see that the first term is $\"c%5E2\"$ and the last term is $\"60\"$ where the coefficients are 1 and 60 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient 60 to get 60. Now what two numbers multiply to 60 and add to the middle coefficient 19? Let's list all of the factors of 60:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 60:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,5,6,10,12,15,20,30,60\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60 ...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 60\r
\n" ); document.write( "\n" ); document.write( "1*60\r
\n" ); document.write( "\n" ); document.write( "2*30\r
\n" ); document.write( "\n" ); document.write( "3*20\r
\n" ); document.write( "\n" ); document.write( "4*15\r
\n" ); document.write( "\n" ); document.write( "5*12\r
\n" ); document.write( "\n" ); document.write( "6*10\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-60)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(-30)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(-20)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(-15)\r
\n" ); document.write( "\n" ); document.write( "(-5)*(-12)\r
\n" ); document.write( "\n" ); document.write( "(-6)*(-10)\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 19? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 19\r
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First Number	Second Number	Sum
1	60	1+60=61
2	30	2+30=32
3	20	3+20=23
4	15	4+15=19
5	12	5+12=17
6	10	6+10=16
-1	-60	-1+(-60)=-61
-2	-30	-2+(-30)=-32
-3	-20	-3+(-20)=-23
-4	-15	-4+(-15)=-19
-5	-12	-5+(-12)=-17
-6	-10	-6+(-10)=-16

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\n" ); document.write( "\n" ); document.write( "From this list we can see that 4 and 15 add up to 19 and multiply to 60\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"c%5E2%2B19c%2B60\"$ , replace $\"19c\"$ with $\"4c%2B15c\"$ (notice $\"4c%2B15c\"$ adds up to $\"19c\"$ . So it is equivalent to $\"19c\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"c%5E2%2Bhighlight%284c%2B15c%29%2B60\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"c%5E2%2B4c%2B15c%2B60\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%28c%5E2%2B4c%29%2B%2815c%2B60%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"c%28c%2B4%29%2B15%28c%2B4%29\"$ Factor out the GCF of $\"c\"$ out of the first group. Factor out the GCF of $\"15\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28c%2B15%29%28c%2B4%29\"$ Since we have a common term of $\"c%2B4\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"c%5E2%2B4c%2B15c%2B60\"$ factors to $\"%28c%2B15%29%28c%2B4%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"c%5E2%2B19c%2B60\"$ factors to $\"%28c%2B15%29%28c%2B4%29\"$ (since $\"c%5E2%2B19c%2B60\"$ is equivalent to $\"c%5E2%2B4c%2B15c%2B60\"$ )\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"c%5E2%2B19c%2B60\"$ factors to $\"%28c%2B15%29%28c%2B4%29\"$ \r
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