# Ch 6: Explorations in Core Math Algebra 1 Chapter 6: Exponents and Polynomials

### About This Chapter

## How It Works:

- Find the lesson within this chapter that corresponds to what you're studying in the Exponents and Polynomials chapter of your textbook.
- Watch fun videos that cover the exponents and polynomials you need to learn or review.
- Complete the quiz after watching each video lesson 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.

## Chapter Topics

You'll learn all of the algebra topics covered in the textbook chapter, including:

- Identifying the five main exponent properties
- Understanding real, rational and irrational numbers
- Proofs for closed sets and irrational sums
- Working with radicands, radical expressions and rational exponents
- How to simplify expressions with rational exponents, square roots of powers
- Defining polynomials, binomials, polynomial functions, and quadratics
- Performing operations with polynomials
- Formula and explanation for special product

*Explorations in Core Math Algebra 1 is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 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. What are Real Numbers? - Definition & Properties

There are many definitions of real numbers, but they all lead to the same conclusion. Real numbers are numbers that have a measurable value. Learn more about real numbers with some examples and a quiz to test your knowledge.

### 3. What are Rational Numbers? - Definition & Examples

In this lesson, we will learn about rational numbers and their characteristics. We'll discover what they are, what they aren't and how to distinguish them from other types of numbers.

### 4. What are Irrational Numbers? - Definition & Examples

Irrational numbers may not be crazy, but they do sometimes bend our minds a little. Learn about common irrational numbers, like the square root of 2 and pi, as well as a few others that businessmen, artists, and scientists find useful.

### 5. Proving That a Set Is Closed

In this lesson, we prove the set of rational numbers is closed under the operation of addition. Following the proof, we deduce that a number having a terminating decimal representation is rational.

### 6. Proving That a Sum Is Irrational

This lesson will briefly review the definitions of rational and irrational numbers. We will then look at how to prove that a sum is irrational based on its addends being rational or irrational.

### 7. Radicands and Radical Expressions

It's easy to see that funky radical symbol and panic just a little bit. There are so many rules that go along with it, it's hard to keep up with them all. This lesson will help by describing what you should do when you are faced with a square root.

### 8. 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.

### 9. Simplifying Square Roots of Powers in Radical Expressions

Simplifying radical expressions that contain powers can be tricky. There are a few simple rules that will help you perform these simplifications with ease. This lesson will teach you how.

### 10. 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!

### 11. 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.

### 12. What are Polynomials, Binomials, and Quadratics?

What do polynomials, binomials, and quadratics have in common? What are their differences? How can you identify each of them? Watch this video lesson to find the answers.

### 13. 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!

### 14. Multiplying Binomials Using FOIL and the Area Method

From the distributive property, to FOIL, to the area model, to happy faces and claws, there are many different ways to learn how to multiply binomials. In this lesson, you'll learn how to use all of them and get to pick which one you like the most.

### 15. Special Product: Definition & Formula

In this lesson, we will review what a binomial is and how to multiply two binomials together. We will then discuss special cases called special products.

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### Other Chapters

Other chapters within the Explorations in Core Math - Algebra 1: Online Textbook Help course

- Explorations in Core Math Algebra 1 Chapter 1: Equations
- Explorations in Core Math Algebra 1 Chapter 2: Inequalities
- Explorations in Core Math Algebra 1 Chapter 3: Functions
- Explorations in Core Math Algebra 1 Chapter 4: Linear Functions
- Explorations in Core Math Algebra 1 Chapter 5: Systems of Equations and Inequalities
- Explorations in Core Math Algebra 1 Chapter 7: Factoring Polynomials
- Explorations in Core Math Algebra 1 Chapter 8: Quadratic Functions and Equations
- Explorations in Core Math Algebra 1 Chapter 9: Exponential Functions
- Explorations in Core Math Algebra 1 Chapter 10: Data Analysis