# Ch 6: Using Exponents and Polynomials

### About This Chapter

## How it works:

- Identify which concepts are covered on your exponents and polynomials homework.
- Find videos on those topics within this chapter.
- Watch fun videos, pausing and reviewing as needed.
- Complete sample problems and get instant feedback.
- Finish your exponents and polynomials homework with ease!

## Topics from your homework you'll be able to complete:

- Identify the five main exponent properties
- Define zero and negative exponents
- Simplify expressions with exponents and rational exponents
- Share the meaning of rational exponents and explain why they are used
- Graph cubics, quartics and quintics
- Add, subtract and multiply polynomials
- Use long and synthetic division to divide polynomials

### 1. What Are the Five Main Exponent Properties?

We'll look at the five important exponent properties and an example of each. You can think of them as the order of operations for exponents. Learn how to handle math problems with exponents here!

### 2. How to Define a Zero and Negative Exponent

The zero and negative exponent properties are two you will use quite a lot in mathematics. The negative exponent property can be confusing, but when you remember a couple fun ideas, you will get it right every time!

### 3. How to Simplify Expressions with Exponents

In this video, we will put all of the exponent properties we have learned together. Don't let lots of numbers and letters confuse you! Simplifying exponents can be easy and fun!

### 4. Rational Exponents

In this video, learn how to go from a rational exponent to a radical expression and back. No tricks or magic, just good math! We'll review the basics and look at a few examples.

### 5. Simplifying Expressions with Rational Exponents

Simplifying expressions with rational exponents is so easy. In fact, you already know how to do it! We simply use the exponent properties but with fractions as the exponent!

### 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. 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!

### 8. 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!

### 9. 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!

### 10. 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!

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### Other Chapters

Other chapters within the Learning Calculus: Basics & Homework Help course

- Understanding the Basics of Functions
- Overview of Graphing & Functions
- Understanding Sequences & Series
- Overview of Continuity
- Understanding Exponentials & Logarithms
- Understanding Applications of Derivatives
- Overview of Differential Equations
- Calculating the Area Under the Curve and Integrals
- Understanding Graphing Derivatives & L'Hopital's Rule
- Integrations in Calculus
- Basics of Geometry & Trigonometry