Factorization of polynomials is the process of breaking down a polynomial into a product of simpler polynomials, often called "factors." This process is similar to factoring numbers into their prime components. The goal of factorization is to express the polynomial as a product that is easier to work with or to solve equations involving the polynomial.
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A polynomial factorization expresses a polynomial as a product of other polynomials. The allowed coefficients matter: has no nonconstant factorization over the rational numbers, but factors as over the real numbers. Difference of squares gives over any commutative ring.