Welcome to an exhilarating journey through the world of Polynomial Functions!

This comprehensive lesson plan is packed with 210 slides designed to guide you through everything you need to know about polynomials, from the foundational Properties of Exponents to the advanced Remainder and Factor Theorems. Along the way, you’ll dive into operations, division, graphing, and solving polynomial equations, all while uncovering the secrets behind Roots and Zeros. With detailed exercises, eye-catching graphs, and real-world applications, this plan will make sure your students not only master polynomial functions but also develop a deep understanding of their behavior and applications in mathematics. Whether you're analyzing graphs, solving equations, or exploring the Rational Zero Theorem, this resource is the key to unlocking polynomial power! Ready to make polynomials fun and engaging? Let’s get started!

Topic Objectives

6-1 Properties of Exponents

• Multiply and Divide Monomials
• Simplify Expressions with Multiplication
• Simplify Expressions with Division
• Simplify Expressions with Powers
• Simplify Expressions Using Several Properties

6-2 Operations with Polynomials

• Determine the Degree of a Polynomial
• Simplify Polynomials
• Multiply Polynomials Horizontally
• Multiply Polynomials Vertically

6-3 Dividing Polynomials

• Divide a Polynomial by a Monomial
• Perform Division Algorithm
• Perform Synthetic Division
• Perform Synthetic Division When Divisor with First Coefficient Other than 1

6-4 Polynomial Functions

• Find Degrees and Leading Coefficients
• Evaluate Function Values of Variables
• Understand the Graphs of Polynomial Functions
• Describe the Graphs of Polynomial Functions

6-5 Analyzing Graphs of Polynomial Functions

• Analyze Graphs of Polynomial Functions
• Graph Polynomial Functions
• Locate Zeros of a Function
• Determine Maximum and Minimum Points
• Graph Polynomial Functions Using TI-84 Graphing Calculator

6-6 Solving Polynomial Equations

• Factor Polynomials
• Determine GCF
• Factoring by Grouping
• Rewrite Polynomials in Quadratic Form
• Solve Equations Using Quadratic Form

6-7 The Remainder and Factor Theorems

• Understand the Remainder Theorem
• Demonstrate Synthetic Substitution
• Demonstrate the Factor Theorem
• Find All Factors Using the Factor Theorem and Synthetic Substitution

6-8 Roots and Zeros

• Understand the Types of Roots
• Determine Number and Type of Roots
• Understand and Apply René Descartes Rule of Signs
• Find Numbers of Positive and Negative Zeros
• Use Synthetic Substitution to Find Zeros
• Understand and Apply the Complex Conjugates Theorem
• Use Zeros to Write a Polynomial Function

6-9 Rational Zero Theorem

• Understand and Apply the Rational Zero Theorem
• List the Possible Rational Zeros of a Function.
• Find Rational Zeros