# Ch 15: Polynomial Function Basics in Precalculus

### About This Chapter

## Polynomial Function Basics in Precalculus - Chapter Summary and Learning Objectives

Learning precalculus is a process that requires a lot of time and dedication. Sometimes, it helps to get assistance outside of your classroom to boost your comprehension and reinforce concepts. In this chapter are lessons designed to help you better understand polynomial function basics in precalculus. Take time to learn the terminology, definitions and mathematical operations associated with this subject area. Top instructors explore function notation, polynomial graphs and the behavior of polynomials. Also, closely examine Pascal's triangle and the binomial theorem.

To make your journey through this chapter simple, review the lessons as fun videos or full transcripts. Timelines are available that allow you to identify and skip to key topics within the videos without watching them in full. Review lessons in any sequence and as often as you'd like. At any time, feel free to test your knowledge of the subject matter by taking quizzes and a chapter exam. In no time, you will have a better grasp of:

- Terminology associated with polynomial functions and how to evaluate a polynomial in function notation
- Properties, factoring, exponential and simplifying polynomial functions
- How to understand basic polynomial graphs and find intervals of polynomial functions
- Short-run and long-run behavior of polynomials and how to graph cubics, quartics, quintics and beyond
- The definitions of Pascal's triangle and the binomial theorem

Video | Objective |
---|---|

Terminology of Polynomial Functions | Explain the meaning and terminology and explore examples of polynomial functions. |

How to Evaluate a Polynomial in Function Notation | Discuss the process of evaluating a polynomial in function notation. |

Polynomials Functions: Properties and Factoring | Describe how to use properties of quadratic functions and do simple factoring. |

Polynomials Functions: Exponentials and Simplifying | Identify and describe properties of exponentials, and discuss how to use them to simplify problems. |

Understanding Basic Polynomial Graphs | Study various ways to graph polynomials and polynomial functions. |

Finding Intervals of Polynomial Functions | Examine the process of finding the intervals on which the function's values are positive and negative. |

Short Run & Long Run Behavior of Polynomials: Definition & Examples | Understand the meaning and how to illustrate the short-run and long-run behavior of polynomials. |

How to Graph Cubics, Quartics, Quintics and Beyond | Learn how to graph cubics, quartics, quintics and more. |

Pascal's Triangle: Definition and Use with Polynomials | Discover the meaning and how to use Pascal's triangle. |

The Binomial Theorem: Defining Expressions | Find out the definition of binomial expressions used in the binomial theorem. |

### 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. Polynomial Functions: Properties and Factoring

Everything from projectile motion to trigonometric functions can be described by polynomials. Review factoring, polynomials and quadratic functions in this lesson.

### 4. Polynomial Functions: Exponentials and Simplifying

How do we keep track of a rapidly multiplying population of bunnies? Well, those are simply powers of 2. Review powers and simplify problems with exponents in this lesson.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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!

### 9. 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.

### 10. 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 Honors Precalculus Textbook course

- Working with Linear Equations
- Working With Inequalities
- Absolute Value Equations
- Working with Complex Numbers
- Systems of Linear Equations
- Mathematical Modeling for Precalculus
- Introduction to Quadratics
- Working with Quadratic Functions
- Geometry Basics for Precalculus
- Types of Functions in Precalculus
- Understanding Function Operations
- Graphing Functions in Precalculus
- Graph Symmetry
- Rate of Change
- Higher-Degree Polynomial Functions
- Rational Functions & Difference Quotients
- Rational Expressions & Function Graphs in Precalculus
- Exponential Functions & Logarithms in Precalculus
- Using Trigonometric Functions
- Trigonometric Graphs
- Solving Trigonometric Equations
- Trigonometric Identities
- Trigonometric Applications
- Graphing Piecewise Functions in Precalculus
- Vectors in Precalculus
- Matrices and Determinants in Algebra
- Understanding Arithmetic Sequences & Series
- Understanding Geometric Sequences & Series
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations
- Working with Sequences & Series
- Sets & Probability
- Continuity
- Limits in Precalculus