\(x^3-7x-6\)
\(=x^3+2x^2-2x^2-4x-3x-6\)
\(=x^2\left(x+2\right)-2x\left(x+2\right)-3\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-2x-3\right)\)
\(=\left(x+2\right)\left(x^2+x-3x-3\right)\)
\(=\left(x+2\right)\left[x\left(x+1\right)-3\left(x+1\right)\right]\)
\(=\left(x+2\right)\left(x+1\right)\left(x-3\right)\)