\(P=x^4-6x^3+12x^2-14x+3\)
\(=x^4-4x^3-2x^3+x^2+8x^2+3x^2-2x-12x+3\)
\(=\left(x^4-4x^3+x^2\right)-\left(2x^2-8x^2+2x\right)+\left(3x^2-12x+3\right)\)
\(=x^2\left(x^2-4x+1\right)-2x\left(x^2-4x+1\right)+3\left(x^2-4x+1\right)=\left(x^2-4x+1\right)\left(x^2-2x+3\right)\)