Factorization of polynomials in hyperbolic geometry and dynamics

Using factorization theorems for sparse polynomials, we compute the trace field of Dehn fillings of the Whitehead link, and (assuming Lehmer’s Conjecture) the minimal polynomial of the small dilatation pseudo-Anosov maps and the trace field of fillings of the figure-8 knot. These results depend on the degrees of the trace fields over Q being sufficiently large.