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*4.6.2. Factorization of Polynomials

Let us now consider the problem of factoring polynomials, not merely finding the greatest common divisor of two or more of them.

Factoring modulo p. As in the case of integer numbers (Sections 4.5.2, 4.5.4), the problem of factoring seems to be more difficult than finding the greatest common divisor. But factorization of polynomials modulo a prime integer p is not as hard to do as we might expect. It is much easier to find the factors of an arbitrary polynomial of degree n, modulo 2, than to use any known method to find the factors of an arbitrary n-bit binary number. This surprising situation is a consequence of an instructive factorization algorithm discovered in 1967 by Elwyn R. Berlekamp [Bell System ...

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