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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: \((3x+2)(12x-\Box ) \)

 Dec 11, 2021
 #1
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The answer is 6.

 Dec 11, 2021
 #2
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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.

 Dec 11, 2021

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