Question

What is the missing term in the factorization?

Answer 1

3(2x+5)(2x-5), 5 is the missing term.

Answer 2

ANSWER

The missing term is

$5$


EXPLANATION


The quadratic expression given to us is

$12 {x}^{2} - 75$

We factor 3 to obtain,


$12 {x}^{2} - 75 = 3(4 {x}^{2} - 25)$

We rewrite the expressions in the parenthesis to obtain,

$12 {x}^{2} - 75 = 3( ({2x})^{2} - {5}^{2} )$



Recall that,


${a}^{2} - {b}^{2} = (a + b)(a - b)$



We apply the difference of two squares formula for the expression in the parenthesis to obtain,

$12 {x}^{2} - 75 = 3(2x + 5)(2x - 5) )$



By comparing to,



$12 {x}^{2} - 75 = 3(2x + ?)(2x - 5) )$



The missing term is 5.