Ch 7: Exponents and Polynomials: Tutoring Solution

About This Chapter

The Exponents and Polynomials chapter of this Precalculus Tutoring Solution is a flexible and affordable path to learning about working with exponents and polynomials. These simple and fun video lessons are each about five minutes long and they teach the operations involving exponents and polynomials required in a typical precalculus course.

How it works:

  • Begin your assignment or other precalculus work.
  • Identify the exponents or polynomials concepts 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 precalculus tutoring solution will benefit any student who is trying to learn about using exponents and polynomials and earn better grades. This resource can help students including those who:

  • Struggle with understanding how to simplify expressions with rational exponents, graph numbers with exponents or perform operations with 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 precalculus
  • Don't have access to their math teacher outside of class

Why it works:

  • Engaging Tutors: We make learning 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 precalculus tutor, these video lessons are thoroughly reviewed.
  • Convenient: Imagine a tutor as portable as your laptop, tablet or smartphone. Learn 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

  • Graph basic functions and data.
  • Graph functions of functions.
  • Graph inverse functions.
  • Describe the properties of quadratic functions and factor polynomials.
  • Describe the properties of exponentials and simplify polynomials.
  • Calculate the slopes and tangents of a graph.
  • Use the point-slope formula to find the equation of a line.
  • Learn how to find the horizontal and vertical asymptotes of a curve.
  • Describe the relationship between inverse and implicit functions.

10 Lessons in Chapter 7: Exponents and Polynomials: Tutoring Solution
Test your knowledge with a 30-question chapter practice test
What Are the Five Main Exponent Properties?

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!

How to Define a Zero and Negative Exponent

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!

How to Simplify Expressions with Exponents

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!

Rational Exponents

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.

Simplifying Expressions with Rational Exponents

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!

How to Graph Cubics, Quartics, Quintics and Beyond

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!

How to Add, Subtract and Multiply Polynomials

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!

How to Divide Polynomials with Long Division

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!

How to Use Synthetic Division to Divide Polynomials

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!

Dividing Polynomials with Long and Synthetic Division: Practice Problems

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!

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.