Simplify completely 12 times x to the third power minus 4 times x to the 2nd power plus 8 times x all over negative 2 times x

(12x^3-4x^2+8x) / (-2x) The greatest common factor of the numerator and denominator is - 2x so upon division by GCF of both numerator and denominator you have:

-6x^2+2x-4 and we can now also factor out - 2

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