What non-zero integer must be placed in the square so that the simplified product of these two binomials is a binomial: \((3x+2)(12x-\Box ) \)
The answer is 6.
Using 6, you get: (3x + 2)(12x - 6) = 36x2 - 6x - 12 which is not a binomial.
If you use 8, you get: (3x + 2)(12x - 8) = 36x2 -16 which is a binomial.
Note that the ratio: 3/2 = 12/8.