Question

What is the missing term in the factorization?

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

Can anybody help me asap please?
Thank you

Answer 1

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

Answer 2

ANSWER

The missing term is


`5`


Step-by-step 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.