What non-zero integer must be placed in the square so that the simplified product of these two binomials is a binomial: (3x + 12)(12x - ___)
The answer is: 48.
(3x + 12)(12x - 48) = 36x2 + 144x - 144x - 576 = 36x2 - 576
To create the answer, factor: (3x + 12)(12x - ) = (3)(x + 4)(12)(x - )
Ignoring the numbers that have been factored out for the moment,
to have (x + 4)(x - ) to be a binomial, the middle term must drop out, so this must
become (x + 4)(x - 4).
But there is a 12 factored out of the second factor, so the second factor really is (12 - 48).