posted by Mandana on .
Determine 2 values of k so that trinomials can be factored over integers 36m^2 + 8m + k and 18x^2 - 42y + k.
Not quite sure what you're getting at, but
36m^2 + 8m - 28 = (9m-7)(4m+4)
In fact, given any n,
(9m - (9n+7))(4m + (4n+4)) = 36m^2 + 8m + (36n^2 + 64n + 28)
Assuming that the second one is 42x, not 42y,
(9x-3)(2x-4) = 18x^2 - 42x + 12
I'm sure you can find many more
There's probably some number-theoretic principles that will enable you to find a general formula, but I'd have to study up a bit.