\(x^3-3x^2+1-3x=x^3-3x-3x^2+1=x^3+x^2-4x^2-4x+x+1=x^2\left(x+1\right)-4x\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^2-4x+1\right)=\left(x+1\right)\left[\left(x^2-4x+4\right)-3\right]=\left(x+1\right)\left[\left(x-2\right)^2-\sqrt{3}^2\right]=\left(x+1\right)\left(x-2-\sqrt{3}\right)\left(x-2+\sqrt{3}\right)\)