What is the product of all constants k such that the quadratic x^2 + kx +15 can be factored in the form (x+a)(x+b), where a and b are integers?

Answer 1

You want 2 integers that satisfy

ab = 15

Then

k = a + b.

The possibilities are combinations of

1 and 15

-1 and -15

3 and 5

-3 and -5