ANSWER
The missing term is
[tex]5[/tex]
EXPLANATION
The quadratic expression given to us is
[tex]12 {x}^{2} - 75[/tex]
We factor 3 to obtain,
[tex]12 {x}^{2} - 75 = 3(4 {x}^{2} - 25)[/tex]
We rewrite the expressions in the parenthesis to obtain,
[tex]12 {x}^{2} - 75 = 3( ({2x})^{2} - {5}^{2} )[/tex]
Recall that,
[tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex]
We apply the difference of two squares formula for the expression in the parenthesis to obtain,
[tex]12 {x}^{2} - 75 = 3(2x + 5)(2x - 5) )[/tex]
By comparing to,
[tex]12 {x}^{2} - 75 = 3(2x + ?)(2x - 5) )[/tex]
The missing term is 5.
