+0  
 
0
86
1
avatar

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 - ___)

 May 1, 2022
 #1
avatar+23199 
0

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).

 May 1, 2022

27 Online Users

avatar