About This Chapter
Properties of Polynomials - Chapter Summary and Learning Objectives
Polynomials are really quite simple to work with, as you may already know. The rules that dictate what a polynomial is also keep them simple. However, that doesn't mean that you don't have to study them or learn the important aspects of working with them. That's why we have put together some lessons on polynomials.
To work with polynomials, you need to understand some basics. Let our lessons teach you how to add, subtract and multiply polynomials. Learn the importance of combining like terms, so you can get the polynomial down to its simplest form.
Dividing polynomials can be done a couple ways, so it is helpful to understand both processes. We have lessons covering the division of polynomials using long division and ones that cover using synthetic division. You will get to watch practice problems being solved to ensure that you don't get lost or confused by the process. You can also work out the practice problems yourself, so you can be sure you understand the concepts that you have learned.
If you are interested in learning more about graphing, then let us teach you about graphing cubics, quartics, quintics and other types of polynomial functions. You'll find our lessons are quite helpful in clearing up any confusion you may have had in the past or helping you to learn new concepts, if you are approaching a concept you have never learned about before. All our video lessons are taught by subject matter experts and edited by experienced video professionals. Thanks for watching!
1. 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!
2. 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!
3. 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!
4. 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!
5. 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 Math 102: College Mathematics course
- Math Foundations
- Linear Equations
- Solving and Graphing Inequalities
- Graphing and Factoring Quadratic Equations
- Complex and Imaginary Numbers
- Properties of Exponents
- Simplifying and Solving Rational Expressions
- Properties of Functions
- Logarithms and Exponential Equations
- Probability and Statistics
- Studying for Math 102