# Ch 22: CEOE Advanced Math: Polynomial Functions Basics

### About This Chapter

## CEOE Advanced Math: Polynomial Functions Basics - Chapter Summary

Educational and entertaining, this chapter's lessons will encourage your understanding of the terms associated with polynomial functions, and they'll remind you of the fundamentals of exponents and polynomial graphs. Watch the videos and read over the lesson transcripts for information on the local minimums and maximums of graphs as well as Pascal's Triangle and the binomial theorem. In preparation for the CEOE Advanced Math examination, study this chapter so that you may:

- Understand terminology such as degree and coefficients
- Perform a polynomial evaluation in function notation
- Work with polynomial graphs
- Find intervals and solutions of polynomials
- Explain the short- and long-run behavior of polynomials
- Graph quintics and quartics
- Utilize Pascal's Triangle
- Understand and use the binomial theorem

The lessons are often under ten minutes long, with some exceptions. They're expertly narrated by real-life teaching professionals. Check out the timeline feature under the video screen; this is where you'll locate the main topics of the lessons. While the videos emphasize animation and graphics, the lesson transcripts feature written step-by-step examples that you can review before you go on to sit for the CEOE Advanced Math examination.

### CEOE Advanced Math: Polynomial Functions Basics Chapter Objectives

The computer-administered CEOE Advanced Math examination has one constructed-response assignment and 80 selected-response questions. After studying throughout college and reviewing this chapter's lessons, you could be ready to accurately complete questions on polynomial functions during the Relations, Functions and Algebra subarea of the assessment. This second of five selected-response subareas is equal to 12% of the test score. You must finish the examination with a score of at least 240 within four hours.

### 1. Terminology of Polynomial Functions

After watching this video lesson, you will be able to understand and use the words associated with polynomial functions like a pro. You will see words, such as leading coefficient, and you will immediately know what it is referring to.

### 2. How to Evaluate a Polynomial in Function Notation

This lesson will review how to evaluate polynomials in function notation. Along with an analogy to explain the process, examples will be given and worked during the lesson.

### 3. Understanding Basic Polynomial Graphs

This lesson will cover understanding basic polynomial graphs. The lesson focuses on how exponents and leading coefficients alter the behavior of the graphs.

### 4. Finding Intervals of Polynomial Functions

Watch this video lesson to learn how you can find the intervals of a polynomial function. Also learn how to find out whether each interval is negative or positive.

### 5. Short Run & Long Run Behavior of Polynomials: Definition & Examples

Watch this video lesson to learn how you can use the graph of a polynomial to help you explain the polynomial function. Learn how to explain the behavior of the polynomial at the origin and at the far ends.

### 6. How to Graph Cubics, Quartics, Quintics and Beyond

Finding the graph of a polynomial isn't too hard. If you can graph, you already know the major steps! With a couple rules and helpful memorizing tools, you will be graphing polynomials in no time!

### 7. Pascal's Triangle: Definition and Use with Polynomials

Pascal's Triangle is defined and discussed briefly. Following the introduction to the triangle, its use in expanding polynomial powers is elaborated with examples.

### 8. The Binomial Theorem: Defining Expressions

In this lesson, students will learn the binomial theorem and get practice using the theorem to expand binomial expressions. The theorem is broken down into its parts and then reconstructed.

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### Other Chapters

Other chapters within the OSAT Advanced Mathematics (CEOE) (111): Practice & Study Guide course

- CEOE Advanced Math: Mathematical Reasoning & Ideas
- CEOE Advanced Math: Origins of Math
- CEOE Advanced Math: Absolute Value
- CEOE Advanced Math: Inequalities
- CEOE Advanced Math: Integers
- CEOE Advanced Math: Operations with Fractions
- CEOE Advanced Math: Operations with Decimals
- CEOE Advanced Math: Percents
- CEOE Advanced Math: Rational & Irrational Numbers
- CEOE Advanced Math: Complex Numbers
- CEOE Advanced Math: Properties of Numbers
- CEOE Advanced Math: Exponents & Exponential Expressions
- CEOE Advanced Math: Roots & Radical Expressions
- CEOE Advanced Math: Number Theory
- CEOE Advanced Math: Vectors, Matrices & Determinants
- CEOE Advanced Math: Properties of Functions
- CEOE Advanced Math: Graphing Functions
- CEOE Advanced Math: The Coordinate Graph & Graph Symmetry
- CEOE Advanced Math: Linear Equations
- CEOE Advanced Math: Systems of Linear Equations
- CEOE Advanced Math: Quadratic Functions
- CEOE Advanced Math: Higher-Degree Polynomial Functions
- CEOE Advanced Math: Piecewise, Absolute Value & Step Functions
- CEOE Advanced Math: Rational Expressions & Function Graphs
- CEOE Advanced Math: Exponential & Logarithmic Functions
- CEOE Advanced Math: Measurement
- CEOE Advanced Math: Perimeter & Area
- CEOE Advanced Math: Symmetry, Similarity & Congruence
- CEOE Advanced Math: Properties of Lines
- CEOE Advanced Math: Angles
- CEOE Advanced Math: Triangles
- CEOE Advanced Math: Triangle Theorems & Proofs
- CEOE Advanced Math: Similar Polygons
- CEOE Advanced Math: The Pythagorean Theorem
- CEOE Advanced Math: Circles
- CEOE Advanced Math: Circular Arcs & Measurement
- CEOE Advanced Math: Transformations
- CEOE Advanced Math: Analytic Geometry & Conic Sections
- CEOE Advanced Math: Trigonometric Functions
- CEOE Advanced Math: Trigonometric Graphs
- CEOE Advanced Math: Trigonometric Applications
- CEOE Advanced Math: Limits
- CEOE Advanced Math: Continuity
- CEOE Advanced Math: Rate of Change
- CEOE Advanced Math: Derivative Calculations & Rules
- CEOE Advanced Math: Graphing & Applying Derivatives
- CEOE Advanced Math: Area Under the Curve & Integrals
- CEOE Advanced Math: Integration Techniques
- CEOE Advanced Math: Differential Equations
- CEOE Advanced Math: Data & Graphs
- CEOE Advanced Math: Samples & Populations
- CEOE Advanced Math: Probability
- CEOE Advanced Math: Sets
- CEOE Advanced Math: Statistics
- CEOE Advanced Math: Number Patterns & Sequences
- CEOE Advanced Math: Number Patterns & Series
- CEOE Advanced Math: Discrete Math
- OSAT Advanced Mathematics (CEOE) (111) Flashcards