12x² - 5x - 2
If you multiply the 12 from 12x² by -2 (the last term of the expression)
you get -24
Now find two factors of -24 that has a sum of -5.
that would be -8 and 3
-8 * 3 = -24
-8 + 3 = -5
Add x after those two factors.
now you have -8x and 3x in place of -5x
12x² - 8x + 3x - 2
Now you factor them by the grouping method.
(12x² - 8x) + (3x - 2)
Simplify the terms in parentheses
3x - 2 cannot be simplified
(12x² - 8x) can be factored. Its common factor is 4x. Divide both terms by 4x.
12x²/4x = 3x
-8x/4x = -2
3x and -2 are together in parentheses while 4x is outside because of the distributive property: a(b + c) = ab + ac. If you put 4x as a, 3x as b, and -2 as c, you'd get (4x)(3x) + (4x)(-2). That equals 12x² + -8x, or better written as 12x² - 8x. (Subtraction rule is keep change change so 12x² - 8x is the same as 12x² + -8x where the subtraction sign is changed to addition and positive 8x is changed to negative 8x).
okaaay anyway so now you got
4x(3x - 2) + (3x - 2)
Notice the two identical expressions in parentheses. Collect those expressions and put it as the first factor.
Now you're left with 4x + 1. This is the second factor.
So the answer is (3x - 2)(4x + 1).
