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
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Jim
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