\(3x^3-7x^2+17x-5\)
\(=3x^3-6x^2-x^2+15x+2x-5\)
\(=\left(-6x^2+2x\right)+\left(3x^3+15x\right)-\left(x^2+5\right)\)
\(=-2x\left(3x-1\right)+3x\left(x^2+5\right)-\left(x^2+5\right)\)
\(=-2x\left(3x-1\right)+\left(x^2+5\right)\left(3x-1\right)\)
\(=\left(3x-1\right)\left(-2x+x^2+5\right)\)