document.write( "Question 402893: factor 12s2+11s-5 \n" ); document.write( "

Algebra.Com's Answer #284977 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at $\"12s%5E2%2B11s-5\"$ we can see that the first term is $\"12s%5E2\"$ and the last term is $\"-5\"$ where the coefficients are 12 and -5 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 12 and the last coefficient -5 to get -60. Now what two numbers multiply to -60 and add to the middle coefficient 11? 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, 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 11? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 11\r
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First Number	Second Number	Sum
1	-60	1+(-60)=-59
2	-30	2+(-30)=-28
3	-20	3+(-20)=-17
4	-15	4+(-15)=-11
5	-12	5+(-12)=-7
6	-10	6+(-10)=-4
-1	60	-1+60=59
-2	30	-2+30=28
-3	20	-3+20=17
-4	15	-4+15=11
-5	12	-5+12=7
-6	10	-6+10=4

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -4 and 15 add up to 11 and multiply to -60\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"12s%5E2%2B11s-5\"$ , replace $\"11s\"$ with $\"-4s%2B15s\"$ (notice $\"-4s%2B15s\"$ adds up to $\"11s\"$ . So it is equivalent to $\"11s\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"12s%5E2%2Bhighlight%28-4s%2B15s%29%2B-5\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"12s%5E2-4s%2B15s-5\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%2812s%5E2-4s%29%2B%2815s-5%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"4s%283s-1%29%2B5%283s-1%29\"$ Factor out the GCF of $\"4s\"$ 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( " $\"%284s%2B5%29%283s-1%29\"$ Since we have a common term of $\"3s-1\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"12s%5E2-4s%2B15s-5\"$ factors to $\"%284s%2B5%29%283s-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"12s%5E2%2B11s-5\"$ factors to $\"%284s%2B5%29%283s-1%29\"$ (since $\"12s%5E2%2B11s-5\"$ is equivalent to $\"12s%5E2-4s%2B15s-5\"$ )\r
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\n" ); document.write( "\n" ); document.write( " Answer:\r
\n" ); document.write( "\n" ); document.write( "So $\"12s%5E2%2B11s-5\"$ factors to $\"%284s%2B5%29%283s-1%29\"$
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