Factorization of Polynomials

Since (x + y)(x - y) = x2 - y2, (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

  1. Factorization by Distributive Property
  2. Factorization Involving the Difference of Two Squares
  3. Factorization of a Perfect Square Trinomial
  4. Factorization of a Polynomial Reducible to the Difference of Two Squares
  5. Factorization of Perfect Cube Polynomials
  6. Factorization of Polynomials Involving Sum or Difference of Two Cubes
  7. Factorizing Trinomials by Splitting the Middle Term