x^4+x^2+2x^3++2x+x^2+1+x^2
=x^2(x^2+1)+2x(x^2+1)+(x^2+1)+x^2
=(x^2+2x+1)(x^2+1)+x^2
=(x^2+1)(x+1)^2+(x^2+1)-1
=(x^2+1)((x+1)^2+1)-1