设f(x)=x^3+kx^2-x+3,则f(1)=0,所以1+k-1+3=0,所以k=-3
因此x^3-3x^2-x+3=x^3-x^2-2x^2+2x-3x-3=(x-1)(x^2-2x-3)=(x-1)(x-3)(x+1)