Summary: The factorization problem of a polynomial over the finite field \(\mathbb F_2\) is transformed to a chess game and then an algorithm is designed to analyze and decompose a given polynomial \(f(x)\) as the product of two polynomial with given degrees. The complexity of the algorithm is then analyzed. One advantage of this algorithm is that we can find a factorization of a polynomial which is close to \(f(x)\) (i. e., has less different coefficients with \(f(x)\)) when such a factorization for \(f(x)\) is not feasible.