R.5 Factoring

Miller & Gerken, College Algebra 2e — Pages 56-67

Learning Objectives

  • Factor out the greatest common factor (GCF)

  • Factor by grouping

  • Factor trinomials

  • Factor special patterns (difference of squares, sum/difference of cubes)

Key Concepts

Greatest Common Factor (GCF)

Notes here…​

Factoring Patterns

Pattern Formula

Difference of Squares

\(a^2 - b^2 = (a+b)(a-b)\)

Sum of Cubes

\(a^3 + b^3 = (a+b)(a^2 - ab + b^2)\)

Difference of Cubes

\(a^3 - b^3 = (a-b)(a^2 + ab + b^2)\)

Perfect Square Trinomial

\(a^2 + 2ab + b^2 = (a+b)^2\)

Perfect Square Trinomial

\(a^2 - 2ab + b^2 = (a-b)^2\)

Factoring Trinomials (AC Method)

For \(ax^2 + bx + c\):

  1. Multiply \(a \cdot c\)

  2. Find two numbers that multiply to \(ac\) and add to \(b\)

  3. Rewrite and factor by grouping

Examples

Example 1. Example 1 (p. XX)

Work through textbook example…​

Practice Problems

Problem 1 (p. XX, #YY)

Problem:

My Work:

Answer:

Section Summary

  1. Key point 1

  2. Key point 2

  3. Key point 3

Study Notes

Personal observations and things to remember…​

Next: R.6 Rational Expressions