Gcf factoring

Math

Definition

A factoring method where you identify the greatest common factor (GCF) of all terms in a polynomial and factor it out. This is typically the first step to try when factoring any expression.

How It Works

  1. Identify the GCF of all the coefficients.
  2. Identify the lowest power of each variable common to every term.
  3. Divide each term by the GCF.
  4. Write the expression as the GCF times the remaining polynomial in parentheses.

Examples

  • 6x³ + 9x² = 3x²(2x + 3)
  • 12ab² − 8a²b + 4ab = 4ab(3b − 2a + 1)

Related Terms

Factoring by grouping Factoring trinomials Difference of squares Polynomial operations

Study This Concept

Practice GCF factoring with free review games in these units:

Algebra 1 Unit 7: Factoring