# Ch 15: Polynomial Functions Basics: Help and Review

### About This Chapter

## Who's it for?

Anyone who needs help learning or mastering high school precalculus material will benefit from taking this course. There is no faster or easier way to learn high school precalculus. Among those who would benefit are:

- Students who have fallen behind in understanding polynomials or working with binomial expressions.
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about polynomials
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources

## How it works:

- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Polynomial Functions Basics chapter exam.

## Why it works:

**Study Efficiently**: Skip what you know, review what you don't.**Retain What You Learn**: Engaging animations and real-life examples make topics easy to grasp.**Be Ready on Test Day**: Use the Polynomial Functions Basics chapter exam to be prepared.**Get Extra Support**: Ask our subject-matter experts any polynomial question. They're here to help!**Study With Flexibility**: Watch videos on any web-ready device.

## Students will review:

In this chapter, you'll learn the answers to questions including:

- How do I evaluate a polynomial in function notation?
- What is the procedure for graphing a polynomial?
- How do I graph cubics, quartics and quintics?
- What are the Pascal's triangle and binomial theorems?

### 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.

### 9. Coordinate System in Geometry: Definition & Types

Coordinate systems use 1-dimensional, 2-dimensional and 3-dimensional spaces and coordinates to define points. The ''xy'' coordinate grid is the most common of these systems, which you can learn how to use in this lesson.

### 10. Solving Quartic Equations

Quartic equations are polynomials that have a degree of four. There are several different means of solving quartic equations such as factoring, treating them like quadratics, use of a graphing calculator, and the rational root theorem.

### 11. How to Square a Trinomial

Trinomials are polynomials with three terms. In this lesson, we'll see how to square a trinomial using a formula and learn how the formula is derived - which gives us another way to square a trinomial!

### 12. Combining Like Terms with the Distributive Property

When you have terms in parentheses in your problem, you have to be careful that you always evaluate these terms first before trying to combine like terms. If you don't, you'll get a wrong answer. Learn how to do this in this lesson.

### 13. How to Use the Distributive Property with Fractions

The distributive property works the same with or without fractions. In this lesson, you'll learn how to use the distributive property on fractions, step by step.

### 14. Solving Quadratic Equations by Completing the Square

After reading this how to lesson, you'll be well on your way to using the completing the square method of solving quadratic equations. Learn what numbers you need to focus on to find your missing square.

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### Other Chapters

Other chapters within the High School Precalculus: Help and Review course

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