Which of the following is a factor of the expression 24x^2-30x-9? Group of answer choices

12x+1

4x-3

2x+3

4x+1

4x + 1

Step-by-step explanation:

24x² - 30x - 9 ( factor out 3 from each term )

= 3(8x² - 10x - 3) ← factor the quadratic

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 8 × - 3 = - 24 and sum = - 10

the factors are + 2 and - 12

use these factors to split the x- term

8x² + 2x - 12x - 3 ( factor the first/second and third/fourth terms )

= 2x(4x + 1) - 3(4x + 1) ← factor out (4x + 1) from each term

= (4x + 1)(2x - 3)

then

24x² - 30x - 9 = 3(4x + 1)(2x - 3) ← in factored form

so (4x + 1) is a factor of the expression

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