  Motivated by coding applications,two enumeration problems are considered: the
number of distinct divisors of a degree-m polynomial over F = GF(q), and the
number of ways a polynomial can be written as a product of two polynomials of
degree at most n over F. For the two problems, bounds are obtained on the
maximum number of factorizations, and a characterization is presented for
polynomials attaining that maximum. Finally, expressions are presented for the
average and the variance of the number of factorizations, for any given m
(respectively, n).
