6x^3+x^2-1=6x^3-2x^2+4x^2-2x+2x-1=(6x^3-2x^2)+(4x^2-2x)+(2x-1)=2x^2(3x-1)+2x(2x-1)+(2x-1)=(2x^2+2x+1)(2x-1)所以能被2x-1整除。