\(x^2+2xy-8y^2+2xz+14yz-3z^2\)
\(=\left(x^2+y^2+z^2+2xy+2xz+2yz\right)+\left(-9x^2+12yz-4x^2\right)\)
\(=\left(x+y+z\right)^2-\left[\left(3x\right)^2-2.3x.2y+\left(2x\right)^2\right]\).
\(=\left(x+y+z\right)^2-\left(3y-2x\right)^2\)
\(=\left(x+y+z-3y+2x\right)\left(x+y+z+3y-2x\right)\)