x^4+x^3-x^2-4x+3
=x^4-x^3-x^2+2x^3-4x+3
=x^2(x^2-x-1)+2x^3-4x+3
=2x^3-4x+3
=2x^3-2x^2-2x+2x^2-2x+3
=2x(x^2-x-1)+2(x^2-x-1)+5
=5