  Let $I\subset \mathbb C[x,y,z]$ be an ideal of height 2 and minimally
generated by three homogeneous polynomials of the same degree. If $I$ is a
locally complete intersection we give a criterion for $\mathbb C[x,y,z]/I$ to
be arithmetically Cohen-Macaulay. Since the setup above is most commonly used
when $I=J_F$ is the Jacobian ideal of the defining polynomial of a
"quasihomogeneous" reduced curve $Y=V(F)$ in $\mathbb P^2$, our main result
becomes a criterion for freeness of such divisors. As an application we give an
upper bound for the degree of the reduced Jacobian scheme when $Y$ is a free
rank 3 central essential arrangement, as well as we investigate the connections
between the first syzygies on $J_F$, and the generators of $\sqrt{J_F}$.
