factor the following 4x^3-6x^2+12x?

2x(2x^2-3x+6)

2x( 2x^2- 3x+ 4)

4x^3 - 6x^2 + 12x
= 2(2x^3 - 3x^2 + 6x)
= 2x(2x^2 - 3x + 6)

4x^3-6x^2+12x = 2x( 2x^2-3x+6) No further factorisation is possible from here. as the discriminant of the quadratic in the bracket is -ve.