Factoring very-high-degree polynomials

In this article, we discuss the current status of polynomial factoring (root finding) algorithms with some historical and mathematical background including size limits, convergence, accuracy and speed. The methods of root approximation versus root refinement are also examined. We then focus on two improved general purpose computational techniques, and in particular the factorization algorithm by Lindsey-Fox (L-F), which makes use of the fast Fourier transform to factor polynomials with random coefficients of degrees as high as 1 million. The mathematics involved here draws only from basic algebra and calculus, the arithmetic of complex numbers , and thus should be accessible to a broad audience.