TL;DR: The Lindsey-Fox algorithm is a very efficient procedure for factoring very high degree polynomials that are reasonably well conditioned that is easily implemented on a parallel computer.
Abstract: The Lindsey-Fox algorithm is a very efficient procedure for factoring very high degree polynomials that are reasonably well conditioned. It conducts a grid search by evaluating the polynomial using the fast Fourier transform (FFT) of the coefficients. The structure of the algorithm is such that it is easily implemented on a parallel computer. We present results of implementations on an AMD cluster and on a Cray XD1. The highest degree random coefficient polynomial factored so far is of 4 million.