\(x^4+x^3+x^2+2\)
\(=x^4+2x^3-x^3-2x^2+2x^2+x^2+2x-2x+2\)
\(=\left(x^4+2x^3+2x^2\right)-\left(x^3+2x^2+2x\right)+\left(x^2+2x+2\right)\)
\(=x^2\left(x^2+2x+2\right)-x\left(x^2+2x+2\right)+\left(x^2+2x+2\right)\)
\(=\left(x^2+2x+2\right)\left(x^2-x+1\right)\)