  Parametric factorizations of linear partial operators on the plane are
considered for operators of orders two, three and four. The operators are
assumed to have a completely factorable symbol. It is proved that
``irreducible'' parametric factorizations may exist only for a few certain
types of factorizations. Examples are given of the parametric families for each
of the possible types. For the operators of orders two and three, it is shown
that any factorization family is parameterized by a single univariate function
  (which can be a constant function).
