Factors of Sparse Polynomials are Sparse

This paper was removed due to an error in the proof (Claim 4.12 as stated is not true). The authors would like to thank Ilya Volkovich for pointing out a counterexample to this paper's main result in positive characteristic: If $F$ is a field with prime characteristic $p$, then the polynomial $x_1^p + x_2^p + \ldots + x^n^p$ has the following factor: $(x_1+x_2+ \ldots + x_n)^{p-1}$, which has sparsity $n^p$.