Perform the long division algorithm . . . . if it is hard, resort to factoring.

you have to factor 4x^3 -10x^2 -8x +6;

Well, it factors to 2(x + 1)(2x - 1)(x - 3), that means if you factor (x - 3),

you are left with 2(x + 1)(2x - 1), right?

Then, 2(x + 1)(2x - 1) = 2(2x^2 + x - 1) = 4x^2 + 2x - 2.

Thus, (4x^3 -10x^2 -8x +6)/(x - 3) = (4x^2 + 2x - 2).

dividend divisor quotient