# Ch 6: Working with Exponents and Polynomials: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other college algebra work.
- Identify the working with exponents and polynomials chapter that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our College Algebra Tutoring Solution will benefit any student who is trying to learn about working with exponents and polynomials and earn better grades. This resource can help students including those who:

- Struggle with understanding exponent properties, how to work with rational exponents, performing mathematical operations with polynomials or any other topic connected to working with exponents and polynomials
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves failing or close to failing their exponents and polynomials unit
- Cope with ADD or ADHD
- Want to get ahead in college algebra
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors:**We make learning how to work with exponents and polynomials simple and fun.**Cost Efficient:**For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality:**Unlike a live algebra tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn how to work with exponents and polynomials on the go!**Learn at Your Pace:**You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning objectives

- Learn the five main exponent properties.
- Define a zero and negative exponent.
- Review how to simplify expressions with exponents.
- Study how to simplify expressions containing rational exponents.
- Explore how to graph cubics, quartics, quintics and more.
- Find out how to add, subtract and multiply polynomials.
- Learn how to divide polynomials with long and synthetic division.

### 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 College Algebra: Tutoring Solution course

- Overview of Linear Equations: Tutoring Solution
- Solving Matrices and Absolute Value: Tutoring Solution
- Overview of Inequalities: Tutoring Solution
- Factoring with FOIL, Graphing Parabolas and Solving Quadratics: Tutoring Solution
- Imaginary and Complex Numbers: Tutoring Solution
- Identifying and Working with Functions: Tutoring Solution
- Rational Expressions: Tutoring Solution
- Solving Exponentials and Logarithms: Tutoring Solution
- Factorials and Binomial Theorem: Tutoring Solution
- Calculating Sequences and Series: Tutoring Solution