\(2x^4+12x^3+14x^2-2x-6\)
\(=2\left(x^4+6x^3+7x^2-x-3\right)\)
\(=2\left(x^4+x^3+5x^3+5x^2+2x^2+2x-3x-3\right)\)
\(=2\left[x^3\left(x+1\right)+5x^2\left(x+1\right)+2x\left(x+1\right)-3\left(x+1\right)\right]\)
\(=2\left(x+1\right)\left(x^3+5x^2+2x-3\right)\)