Solving by factoring

Math

Definition

A method for solving polynomial equations by rewriting the polynomial as a product of factors and then setting each factor equal to zero. This relies on the zero product property: if ab = 0, then a = 0 or b = 0.

How It Works

  1. Move all terms to one side so the equation equals zero.
  2. Factor the polynomial completely.
  3. Set each factor equal to zero.
  4. Solve each resulting equation for the variable.

Examples

  • x² − 5x + 6 = 0 factors to (x−2)(x−3) = 0, so x = 2 or x = 3
  • 2x² + 8x = 0 factors to 2x(x+4) = 0, so x = 0 or x = −4

Related Terms

Factoring trinomials Difference of squares Quadratic formula Zeros and multiplicity

Study This Concept

Practice solving by factoring with free review games in these units:

Algebra 1 Unit 8: Quadratic Equations