Factoring

Quadratic expressions may be used to model physical properties of a large bridge, the trajectory of a baseball or rocket, and the revenue and profit of a business. By factoring these expressions, specific characteristics of the model can be identified. In this chapter, you will explore the process of factoring expressions and see how factoring is used to solve certain types of equations.

Sections

• Greatest Common Factor and Factor by Grouping — finding the greatest common factor of two or more expressions, factoring the greatest common factor from a polynomial, and factoring by grouping.
• Factor Trinomials of the Form $x^2+bx+c$ — factoring trinomials whose leading coefficient is $1$, including those with two variables.
• Factor Trinomials of the Form $ax^2+bx+c$ — factoring trinomials with a leading coefficient other than $1$ by trial and error and by the “ac” method, after first factoring out any greatest common factor.
• Factor Special Products — factoring perfect square trinomials, factoring differences of squares, and factoring sums and differences of cubes.
• General Strategy for Factoring Polynomials — recognizing and applying the appropriate factoring method for any polynomial.
• Quadratic Equations — using the Zero Product Property to solve quadratic equations by factoring and solving applications modeled by quadratic equations.

This chapter overview is adapted from Elementary Algebra 2e, Chapter 7 Introduction by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, © OpenStax, licensed under CC BY-NC-SA 4.0. Access the original for free at openstax.org. Changes: condensed the chapter introduction and recast the chapter outline as a section list.