  We give a complete factorization of the invariant factors of resultant
matrices built from birational parameterizations of rational plane curves in
terms of the singular points of the curve and their multiplicity graph. This
allows us to prove the validity of some conjectures about these invariants
stated by Chen, Wang and Liu in [J. Symbolic Comput. 43(2):92-117, 2008]. As a
byproduct, we also give a complete factorization of the D-resultant for
rational functions in terms of the similar data extracted from the
multiplicities.
