We are looking to factor 23x^2 + kx - 5 + x^2 - 3. Some values of k allow us to factor it as a product of linear binomials with integer coefficients. what are all such values of k?
24x^2 + kx - 8.
Factors of 24: 1, 24. 2, 12. 3, 8. 4, 6.
(x )(24x ) or (2x _ _)(12x _ _), etc
You could so something like this while plugging in factors of 8 into the blank spots and adding opposite parity operations. (_x + 4)(_x - 2) etc.