Factorization of Polynomials

Since (x + y)(x – y) = x2 – y2, you can say that (x + y) and (x – y) are factors of the product (x2 – y2).

Factorization of a polynomial is a process of writing the polynomial as a product of two (or more) polynomials. Each polynomial in the product is called a factor of the given polynomial.

A polynomial is said to be completely factored if none of its factors can be further expressed as a product of two polynomials of lower degree and if the integer coefficients have no common factor other than 1 or –1.

Thus, complete factorization of (x2 – 4x) is x(x–4).

On the other hand the factorization (4x2 – 1)(4x2 + 1) of (16x4 – 1) is not complete since the factor (4x2 – 1) can be further factorized as (2x – 1)(2x + 1). Thus, complete factorization of (16x4 – 1) is (2x – 1)(2x + 1)(4x2 + 1).

Methods of Factorization

  • Factorization by Distributive Property
  • Factorization Involving the Difference of Two Squares
  • Factorization of a Perfect Square Trinomial
  • Factorization of a Polynomial Reducible to the Difference of Two Squares
  • Factorization of Perfect Cube Polynomials
  • Factorization of Polynomials Involving Sum or Difference of Two Cubes
  • Factorizing Trinomials by Splitting the Middle Term