Question

How do I find a value for k that will make the expression factorable.
36x^2 + 8x + k?

Answer 1

Clearly, k=0 will do the job, but I doubt that's what you want.

the quadratic formula says

x = (-8±√(64-144k))/72

So, any negative value of k which makes 64-144k a perfect square will work. SO, if we let v be 64-144k, we have

k v
-1 208
-2 352
-3 496
-4 640
-5 784 = 28^2

36x^2+8x-5 = (2x+1)(18x-5)

There are, of course, many other workable values.