Answer: (x - 4) (3x + 2)
Explanation:
Factor 3x² - 10x - 8
a) Multiply the first and last coefficients: 3(-8) = -24
b) Find two numbers whose product equals -24 and sum equals -10 (the middle coefficient).
-24
∧
1 -24
2 -12 This works!
c) Replace the the middle term of -10x with 2x - 12x
3x² + 2x - 12x - 8
d) Split the equation into two sections (left and right) and factor each side separately.
3x² + 2x - 12x - 8
x(3x + 2) -4(3x + 2)
e) Notice that the parenthesis are the same. The values on the outside combine to make one of the factors and the parenthesis are the other factor.
x(3x + 2) -4(3x + 2)
= (x - 4) (3x + 2)