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I NEED HALP ON BINOMIALS!! PLS ASLO EXPLAIN SOLUTION

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What non-zero integer must be placed in the square so that the simplified product of these two binomials is a binomial: $$(3x+2)(12x-\Box )$$

Apr 17, 2022

\begin{align*} (3x+2)(12x-\Box) &= (3x)(12x) +(3x)(-\Box) +2(12x) - 2\cdot\Box\\ &=36x^2 -(3\cdot\Box)x + 24x - 2\cdot \Box. \end{align*}
In order for this to be a binomial, the two $$x$$ terms must cancel. Therefore, we must have $$3\cdot \Box = 24$$, which means $$\Box = \boxed{8}$$.