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3 votes
What is the missing term in the factorization?

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

Can anybody help me asap please?
Thank you

2 Answers

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

User Andraaspar
by
7.8k points
4 votes
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.

User UtterlyConfused
by
7.6k points

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