# Ch 6: McDougal Littell Algebra 2 Chapter 6: Polynomials and Polynomial Functions

### About This Chapter

## How it works:

- Identify the lessons in the McDougal Littell Algebra 2 Polynomials and Polynomial Functions chapter with which you need help.
- Find the corresponding video lessons within this companion course chapter.
- Watch fun videos that cover the polynomials and polynomial functions topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.

## Students will learn:

- Exponential notation
- Methods for simplifying exponential expressions
- The order of operations
- Multiplication and division of exponential expressions
- The power of zero
- Negative exponents
- Power of powers
- Basic polynomial graphs
- Basic transformations for polynomial graphs
- Multiplication and division of polynomials
- Properties of polynomial functions
- Steps to factor by grouping
- Division of polynomials using long and synthetic division
- The Remainder Theorem and Factor Theorem
- The Rational Zeros Theorem
- The Fundamental Theorem of Algebra
- Graphs of cubics, quartics and quintics

*McDougal Littell Algebra 2 is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 1. How to Use Exponential Notation

Exponential notation is a mathematical method for writing longer multiplication problems in a simplified manner. This lesson will define how to work with exponential notation and give some examples of how it is used.

### 2. Simplifying and Solving Exponential Expressions

What do we do with an exponent? In this lesson, we'll learn how to simplify and solve expressions containing exponents. We'll solve a variety of types of exponential expressions.

### 3. Exponential Expressions & The Order of Operations

When performing mathematical operations, there is a specific order in which the operations should be performed. This includes when to simplify the exponents. This lesson will describe in what order exponents should be solved as you are performing mathematical operations.

### 4. Multiplying Exponential Expressions

There are certain rules that govern working with exponential expressions. This lesson deals with the rule for multiplying exponential expressions. It will describe the rule and give some examples of how it works.

### 5. Dividing Exponential Expressions

Any time you work with expressions that contain exponents, you have to follow a specific set of rules that are not the same as when you are working with expressions that do not contain exponents. This lesson will describe the rules associated with dividing terms that contain exponents.

### 6. The Power of Zero: Simplifying Exponential Expressions

Raising a number to the power of zero is not the same as if the exponent is a number other than zero. This lesson will explain the rule involving using zero as an exponent and will give some examples of how it works.

### 7. Negative Exponents: Writing Powers of Fractions and Decimals

Most numbers can be written in different ways, either as a fraction, decimal or exponent. This lesson will teach you how to write fractions and decimals using exponents and how to convert between the two.

### 8. Power of Powers: Simplifying Exponential Expressions

Mathematics is a very logical science. There is a rule for everything and not many exceptions to those rules. Working with exponents is no different. This lesson will describe the rule for raising a power to a power and also will give some examples in how to solve them.

### 9. 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.

### 10. 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.

### 11. Basic Transformations of Polynomial Graphs

The basic transformations for a graph are movement up and down, left and right, pinched or stretched graphs, and flipped graphs. This lesson will review how to accomplish each of these transformations.

### 12. How to Add, Subtract and Multiply Polynomials

Adding, subtracting and multiplying polynomials are, basically, the same as adding, subtracting and multiplying numbers. They only difference is that we have a pesky variable to worry about, but this video will show you that's no problem, so no worries! This method has worked for many of my students, and I think it will work for you, too!

### 13. 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.

### 14. Factoring By Grouping: Steps, Verification & Examples

How do you factor an expression if all the terms don't share a common factor? Grouping! In this lesson, we'll learn how to use grouping to help factor expressions.

### 15. Factoring Polynomials Using Quadratic Form: Steps, Rules & Examples

Factoring a polynomial of degree 4 or higher can be a difficult task. However, some polynomials of higher degree can be written in quadratic form, and the techniques used to factor quadratic functions can be utilized.

### 16. How to Divide Polynomials with Long Division

Arithmetic long division and polynomial long division are very similar. Yes, it's a long process, but once you have the rhythm you will get every problem correct!

### 17. How to Use Synthetic Division to Divide Polynomials

Synthetic division is a 'short-cut' way of dividing a polynomial by a monomial. You still need to know long division, sorry, but this method is way fun when you're dividing by a monomial!

### 18. Dividing Polynomials with Long and Synthetic Division: Practice Problems

Let's look at some more polynomial division problems. We will use long division and synthetic division, but this time we will have a couple of more involved problems. So, get out some paper and a pencil and let's begin!

### 19. Remainder Theorem & Factor Theorem: Definition & Examples

In this lesson, you will learn about the remainder theorem and the factor theorem. You will also learn how to use these theorems to find remainders and factors of polynomials.

### 20. Finding Rational Zeros Using the Rational Zeros Theorem & Synthetic Division

After completing this lesson, you will know what the rational zeros theorem says. You will also know how to apply this theorem to find zeros of polynomial functions.

### 21. Fundamental Theorem of Algebra: Explanation and Example

In this lesson, you will learn what the Fundamental Theorem of Algebra says. You will also learn how to apply this theorem in determining solutions of polynomial functions.

### 22. 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!

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### Other Chapters

Other chapters within the McDougal Littell Algebra 2: Online Textbook Help course

- McDougal Littell Algebra 2 Chapter 1: Equations and Inequalities
- McDougal Littell Algebra 2 Chapter 2: Linear Equations and Functions
- McDougal Littell Algebra 2 Chapter 3: Systems of Linear Equations and Inequalities
- McDougal Littell Algebra 2 Chapter 4: Matrices and Determinants
- McDougal Littell Algebra 2 Chapter 5: Quadratic Functions
- McDougal Littell Algebra 2 Chapter 7: Powers, Roots, and Radicals
- McDougal Littell Algebra 2 Chapter 8: Exponential and Logarithmic Functions
- McDougal Littell Algebra 2 Chapter 9: Rational Equations and Functions
- McDougal Littell Algebra 2 Chapter 10: Quadratic Relations and Conic Sections
- McDougal Littell Algebra 2 Chapter 11: Sequences and Series
- McDougal Littell Algebra 2 Chapter 12: Probability and Statistics
- McDougal Littell Algebra 2 Chapter 13: Trigonometric Ratios and Functions
- McDougal Littell Algebra 2 Chapter 14: Trigonometric Graphs, Identities, and Equations