Determine the linear factors for 27x^3-12x

27x^3 - 12x factors into

3 (9x^3 - 4x) a common factor of three has been taken out.

3x (9x^2 - 4) a common factor of x has been taken out. 3x is not a linear factor.

9x^2 - 4 factors by means of the difference of squares

3x (3x - 2) (3x + 2)

The two linear factors are 3x - 2 and 3x + 2