Question

factor completely.
$4x^2 - 2x - 2$
select the correct choice below and, if necessary, fill in the answer box to complete your choice
a. $4x^2 - 2x - 2 = \square$
b. the trinomial is prime.

Explanation:

Step1: Factor out GCF

Factor out the greatest common factor of 2 from all terms:
$4x^2 - 2x - 2 = 2(2x^2 - x - 1)$

Step2: Factor the quadratic trinomial

Factor $2x^2 - x - 1$ by finding two numbers that multiply to $2\times(-1)=-2$ and add to $-1$ (these numbers are $-2$ and $1$), then rewrite and factor:
$2x^2 - x - 1 = 2x^2 - 2x + x - 1 = 2x(x-1) + 1(x-1) = (2x+1)(x-1)$

Step3: Combine the factors

Substitute the factored quadratic back into the expression from Step1:
$2(2x+1)(x-1)$

Answer:

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