x4+3x3+3x2+4x+3
=(x^4+x)+(3x^3+3x^2)+(3x+3)
=x(x+1)(x^2-x+1)+3x^2(x+1)+3(x+1)
=(x+1)(x^3-x^2+x+3x^2+3)
=(x+1)(x^3+2x^2+x+3)