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