document.write( "Question 407841: factoring 3x^2-5x-884 \n" ); document.write( "

Algebra.Com's Answer #287384 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 $\"3x%5E2-5x-884\"$ we can see that the first term is $\"3x%5E2\"$ and the last term is $\"-884\"$ where the coefficients are 3 and -884 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 3 and the last coefficient -884 to get -2652. Now what two numbers multiply to -2652 and add to the middle coefficient -5? Let's list all of the factors of -2652:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -2652:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,12,13,17,26,34,39,51,52,68,78,102,156,204,221,442,663,884,1326,2652\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-12,-13,-17,-26,-34,-39,-51,-52,-68,-78,-102,-156,-204,-221,-442,-663,-884,-1326,-2652 ...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 -2652\r
\n" ); document.write( "\n" ); document.write( "(1)*(-2652)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-1326)\r
\n" ); document.write( "\n" ); document.write( "(3)*(-884)\r
\n" ); document.write( "\n" ); document.write( "(4)*(-663)\r
\n" ); document.write( "\n" ); document.write( "(6)*(-442)\r
\n" ); document.write( "\n" ); document.write( "(12)*(-221)\r
\n" ); document.write( "\n" ); document.write( "(13)*(-204)\r
\n" ); document.write( "\n" ); document.write( "(17)*(-156)\r
\n" ); document.write( "\n" ); document.write( "(26)*(-102)\r
\n" ); document.write( "\n" ); document.write( "(34)*(-78)\r
\n" ); document.write( "\n" ); document.write( "(39)*(-68)\r
\n" ); document.write( "\n" ); document.write( "(51)*(-52)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(2652)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(1326)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(884)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(663)\r
\n" ); document.write( "\n" ); document.write( "(-6)*(442)\r
\n" ); document.write( "\n" ); document.write( "(-12)*(221)\r
\n" ); document.write( "\n" ); document.write( "(-13)*(204)\r
\n" ); document.write( "\n" ); document.write( "(-17)*(156)\r
\n" ); document.write( "\n" ); document.write( "(-26)*(102)\r
\n" ); document.write( "\n" ); document.write( "(-34)*(78)\r
\n" ); document.write( "\n" ); document.write( "(-39)*(68)\r
\n" ); document.write( "\n" ); document.write( "(-51)*(52)\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 -5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -5\r
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First Number	Second Number	Sum
1	-2652	1+(-2652)=-2651
2	-1326	2+(-1326)=-1324
3	-884	3+(-884)=-881
4	-663	4+(-663)=-659
6	-442	6+(-442)=-436
12	-221	12+(-221)=-209
13	-204	13+(-204)=-191
17	-156	17+(-156)=-139
26	-102	26+(-102)=-76
34	-78	34+(-78)=-44
39	-68	39+(-68)=-29
51	-52	51+(-52)=-1
-1	2652	-1+2652=2651
-2	1326	-2+1326=1324
-3	884	-3+884=881
-4	663	-4+663=659
-6	442	-6+442=436
-12	221	-12+221=209
-13	204	-13+204=191
-17	156	-17+156=139
-26	102	-26+102=76
-34	78	-34+78=44
-39	68	-39+68=29
-51	52	-51+52=1

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\n" ); document.write( "\n" ); document.write( "None of these pairs of factors add to -5. So the expression $\"3x%5E2-5x-884\"$ cannot be factored\r
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\n" ); document.write( "\n" ); document.write( "In other words, the polynomial is prime.\r
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\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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