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