how do you factor 12a²-2a-4?

12a^2 - 2a - 4
= 2(6a^2 - a - 2)
= 2(6a^2 + 3a - 4a - 2)
= 2(2a + 1)(3a - 2)

1st factor:
= 2

2nd factor:
(12a² - 2a - 4)/2 = 0
6a² - a - 2 = 0
6a² - a = 2
a² - 1/6a = 1/3
a² - 1/12a = 1/3 + (1/12)²
a² - 1/12a = 48/144 + 1/144
(a - 1/12)² = 49/144
a - 1/12 = 7/12
= a - 1/12 + 7/12
= a + 1/2
= 2a + 1

3rd factor:
= (6a² - a - 2)/(2a + 1)
= 3a - 2

Answer: Factors: 2 * (2a + 1) * (3a - 2)

well, instead of just giving the answer, i'll tell you how to do it.
this is a trick my algebra 2 teacher taught us. i guess he made it up, the smart fellerr. haha. (:

first, simplify it by dividing by 2
6a²-a-2
multiply 6 and -2 to get -12
then you get 2 numbers that multiply together to give you -12, but also add up to -1, which would be 3 and -4
so you do
2(6a + 3) (6a - 4)
and then simplify the factors
2(2a + 1) (3a - 2)

i hope that's the right answer... haha.

2 (6a² - a - 2)
2 (3a + 2)(a - 1)

12a² - 2a - 4 = 2(3a - 2)(2a + 1)