Question

factor completely
$24x^2 - 4x - 4$

select the correct choice below and, if necessary, fill in the answer box to complete your choice

a. $24x^2 - 4x - 4 = \square$

b. this trinomial is prime.

Explanation:

Step1: Factor out GCF

Factor out 4 from all terms:
$4(6x^2 - x - 1)$

Step2: Factor the quadratic

Find two numbers that multiply to $6\times(-1)=-6$ and add to $-1$ (which are $-3$ and $2$), then split and factor:
$6x^2 - x - 1 = 6x^2 - 3x + 2x - 1 = 3x(2x - 1) + 1(2x - 1) = (3x + 1)(2x - 1)$

Step3: Combine factors

Substitute the factored quadratic back into the expression:
$4(3x + 1)(2x - 1)$

Answer:

A. $24x^2 - 4x - 4 = 4(3x + 1)(2x - 1)$