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

  • Math -

    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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