SOLUTION: factoring 3x^2-5x-884

Question 407841: factoring 3x^2-5x-884
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 3 and -884 respectively.

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:

Factors of -2652:
1,2,3,4,6,12,13,17,26,34,39,51,52,68,78,102,156,204,221,442,663,884,1326,2652

-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

These factors pair up and multiply to -2652
(1)*(-2652)
(2)*(-1326)
(3)*(-884)
(4)*(-663)
(6)*(-442)
(12)*(-221)
(13)*(-204)
(17)*(-156)
(26)*(-102)
(34)*(-78)
(39)*(-68)
(51)*(-52)
(-1)*(2652)
(-2)*(1326)
(-3)*(884)
(-4)*(663)
(-6)*(442)
(-12)*(221)
(-13)*(204)
(-17)*(156)
(-26)*(102)
(-34)*(78)
(-39)*(68)
(-51)*(52)

note: remember, the product of a negative and a positive number is a negative number

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

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

None of these pairs of factors add to -5. So the expression cannot be factored

In other words, the polynomial is prime.

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
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