1.6 More Equations and Applications

Miller & Gerken, College Algebra 2e — Pages 154-167

Learning Objectives

  • Solve polynomial equations by factoring

  • Solve radical equations

  • Solve equations with rational exponents

  • Recognize and check for extraneous solutions

Key Concepts

Higher Degree Polynomial Equations

  1. Set equal to zero

  2. Factor completely

  3. Apply zero product property

  4. Solve each factor

Radical Equations

  1. Isolate the radical

  2. Raise both sides to appropriate power

  3. Solve resulting equation

  4. Check for extraneous solutions

Squaring both sides can introduce extraneous solutions. Always check!

Equations with Rational Exponents

Convert between radical and exponent form:

\[x^{m/n} = \sqrt[n]{x^m}\]

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: 1.7 Linear Inequalities