\(\left(3x^3-8x^2+x+6\right):\left(x-2\right)\\ =\left[\left(3x^3-6x^2\right)-\left(2x^2-4x\right)-\left(3x-6\right)\right]:\left(x-2\right)\\ =\left[3x^2\left(x-2\right)-2x\left(x-2\right)-3\left(x-2\right)\right]:\left(x-2\right)\\ =\left[\left(3x^2-2x-3\right)\left(x-2\right)\right]:\left(x-2\right)\\ =3x^2-2x-3\)