Posted by **Mandana** on Sunday, December 18, 2011 at 9:21am.

Determine 2 values of k so that trinomials can be factored over integers 36m^2 + 8m + k and 18x^2 - 42y + k.

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**Steve**, Sunday, December 18, 2011 at 6:01pm
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.

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