Question 895842: find all integral values of k for which y2-ky-36 can fractored.
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! 
Look at the factors of -36 such that
1, -36
2, -18
3, -12
4, -9
6, -6
9, -4
12, -3
18, -2
36, -1
Then sum them to find 
-35,-16,-9,-5,0,5,9,16,35
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website!
Just use all the ways -36 can be written as the
product of two integer factors:
If k is a NON-NEGATIVE integer, then
these 5 are the only ways
(y+1)(y-36) = y²-35x-36 k=35
(y+2)(y-18) = y²-16x-36 k=16
(y+3)(y-12) = y²-9x-36 k=9
(y+4)(y-9) = y²-5x-36 k=5
(y+6)(y-6) = y²-0x-36 k=0
If k is a NEGATIVE integer, then
these 4 are the only ways
(y-1)(y+36) = y²+35x-36 k=-35
(y-2)(y+18) = y²+16x-36 k=-16
(y-3)(y+12) = y²+9x-36 k=-9
(y-4)(y+9) = y²+5x-36 k=-5
Edwin
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