\(=2x^4-6x^3-x^3+3x^2-5x^2+15x-2x+6\)
\(=2x^3\left(x-3\right)-x^2\left(x-3\right)-5x\left(x-3\right)-2\left(x-3\right)\)
\(=\left(x-3\right)\left(2x^3-x^2-5x-2\right)\)
\(=\left(x-3\right)\left(2x^3-4x^2+3x^2-6x+x-2\right)\)
\(=\left(x-3\right)\left[2x^2\left(x-2\right)+3x\left(x-2\right)+\left(x-2\right)\right]\)
\(=\left(x-3\right)\left(x-2\right)\left(2x^2+3x+1\right)\)
\(=\left(x-3\right)\left(x-2\right)\left(x+1\right)\left(2x+1\right)\)