About This Chapter
Exponents and Polynomials
Do you have some questions about exponents? Are you wondering just what they are and how they're used? Do they flat-out confuse you? Chances are others have these same issues. That's why we've got lessons designed to help you become familiar with this tricky aspect of math. Let them answer all your questions!
In our lessons, you'll see videos that cover the five main exponent properties, defining a zero or negative exponent and simplifying expressions with exponents. Discover why we use the exponent properties. Learn what to do with a zero and negative exponent. Find out how to apply the exponent properties to simplify an expression.
What's a rational exponent? If you don't know, then our lessons will tell you. Watch as our instructor explains why we use them and how to simplify expressions with rational exponents.
If your graphing skills are not up to par, then use our lessons to learn how to graph cubics, quartics, quintics and more. See what such graphing looks like through examples in our lessons.
How do you feel about polynomials? Do you know all about them? Can you solve equations containing them? If you aren't feeling too confident, then watch our lessons and learn how to add, subtract, multiply and divide them. You may also want to catch our lessons covering their synthetic division.
Our lessons are packed with real examples of problems that are solved step-by-step, so you can see exactly what to do. After watching our lessons and solving the example problems, you should be ready to tackle exponents and polynomials on your own.
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!
11. Practice Problem Set for Exponents and Polynomials
If you'd like more opportunities to practice the concepts you've learned in this chapter, please download the following practice problem set. After you've completed the set, you can download the answer key to check your work and help your understanding. Please note that these documents are not permissible for use during your proctored exam.
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Other chapters within the Math 101: College Algebra course
- Foundations of Linear Equations
- Matrices and Absolute Value
- Factoring with FOIL, Graphing Parabolas and Solving Quadratics
- Complex Numbers
- Rational Expressions
- Radical Expressions & Functions
- Exponentials and Logarithms
- Probability Mechanics
- Sequences and Series
- Studying for Math 101