About This Chapter
Who's it for?
Anyone who needs help learning or mastering precalculus material will benefit from taking this course. There is no faster or easier way to learn precalculus. Among those who would benefit are:
- Students who have fallen behind in understanding or working with exponents and polynomials
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about exponents and polynomials
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources
How it works:
- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Exponents and Polynomials chapter exam.
Why it works:
- Study Efficiently: Skip what you know, review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the Exponents and Polynomials chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any exponents and polynomials question. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students will review:
In this chapter, you'll learn the answers to questions including:
- What are the five main properties of exponents?
- What are zero and negative exponents?
- How do I simplify expressions with exponents?
- What is the definition of a rational exponent?
- What are the steps for simplifying expressions with rational exponents?
- How do I graph cubics, quartics and quintics?
- How do I add, subtract and multiply polynomials?
- What are the steps involved in dividing polynomials with long division?
- How do I 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 within the Precalculus: Help and Review course
- Functions in Precalculus: Help and Review
- Evaluating Exponential and Logarithmic Functions: Help and Review
- Inequalities in Precalculus: Help and Review
- Foundations and Linear Equations in Precalculus: Help and Review
- Graphing and Rational Equations: Help and Review
- Factoring and Graphing Quadratic Equations: Help and Review
- Piecewise and Composite Functions: Help and Review
- Geometry and Trigonometry: Help and Review
- Using Scientific Calculators: Help and Review
- Trigonometry: Help and Review