x^4+2x^3+3x^2+2x+1

=x^4+2x^2+1+x^3+x+x^3+x^2+x

=(x^2+1)^2+x(x^2+1)+x(x^2+x+1)

=(x^2+1)(x^2+1+x)+x(x^2+x+1)

=(x^2+x+1)(x^2+x+1)

=(x^2+x+1)^2