  We prove a function field analogue of a conjecture of Schinzel on the
factorization of univariate polynomials over the rationals. We derive from it a
finiteness theorem for the irreducible factorizations of the bivariate Laurent
polynomials in families with fixed set of complex coefficients and varying
exponents. Roughly speaking, this result shows that the truly bivariate
irreducible factors of these sparse Laurent polynomials, are also sparse. The
proofs are based on a variant of the toric Bertini's theorem due to Zannier and
Fuchs, Mantova and Zannier.
