About This Chapter
Operations with Monomials and Polynomials - Chapter Summary
This chapter's video lessons refresh your knowledge of what monomials and polynomials are and how to work with them mathematically. Our professional instructors guide you step-by-step through the process of performing math operations with these expressions.
You'll also take a look at graphs for polynomials and their transformations. A couple of the lessons explain how to use the binomial theorem and Pascal's Triangle as well. After watching the videos in the chapter, you should be prepared to:
- Add, subtract, multiply and divide monomials
- Find the square and cube roots of monomials
- Evaluate polynomials in function notation
- Interpret basic polynomial graphs and transformations
- Graph cubics, quartics and quintics
- Add, subtract and multiply polynomials
- Use Pascal's Triangle to expand polynomials
- Expand binomial exponents using the binomial theorem
- Divide polynomials using long and synthetic division
- Perform operations with polynomials containing several variables
Our short video lessons make learning about monomials and polynomials a straightforward, convenient process. After watching a lesson, use the timeline's jump feature to go back and review certain problems or explanations as needed. In addition to the videos, we provide lesson transcripts as another study tool. You can test your comprehension of the covered material by taking the self-assessment lesson quizzes.
1. What Are Monomials & Polynomials?
Watch this video lesson to learn how coefficients and variables combine to form monomials and polynomials. You'll also find out how the exponent determines the degree of polynomials.
2. How to Add & Subtract Monomials
In this video lesson, you will learn what kinds of monomials you can add or subtract together. You will also learn how to immediately tell when you cannot add or subtract your monomials.
3. How to Multiply & Divide Monomials
In this lesson, we're going to learn how to multiply and divide monomials. As you can imagine, this is a very important skill that much of algebra (and even more advanced math) depends upon.
4. Square & Cube Roots of Monomials
Being able to find the cube or square root of monomials will make algebra, and indeed all math, much easier. However, it's not as hard as you'd think. This lesson will show you how and allow you to test your skills with a quiz.
5. How to Evaluate a Polynomial in Function Notation
This lesson will review how to evaluate polynomials in function notation. Along with an analogy to explain the process, examples will be given and worked during the lesson.
6. Understanding Basic Polynomial Graphs
This lesson will cover understanding basic polynomial graphs. The lesson focuses on how exponents and leading coefficients alter the behavior of the graphs.
7. Basic Transformations of Polynomial Graphs
The basic transformations for a graph are movement up and down, left and right, pinched or stretched graphs, and flipped graphs. This lesson will review how to accomplish each of these transformations.
8. 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!
9. 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!
10. Pascal's Triangle: Definition and Use with Polynomials
Pascal's Triangle is defined and discussed briefly. Following the introduction to the triangle, its use in expanding polynomial powers is elaborated with examples.
11. The Binomial Theorem: Defining Expressions
In this lesson, students will learn the binomial theorem and get practice using the theorem to expand binomial expressions. The theorem is broken down into its parts and then reconstructed.
12. 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!
13. 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!
14. 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!
15. Operations with Polynomials in Several Variables
In this video lesson, you will learn how to handle and work with polynomials that have more than one variable. This is important because in math you sometimes have to work with several variables at the same time.
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Other chapters within the Contemporary Math: Help and Review course
- Mathematical Reasoning & Problem-Solving: Help and Review
- How to Solve Word Problems: Help and Review
- Statistics Overview: Help and Review
- Probability Overview: Help and Review
- Understanding Discrete Probability Distributions: Help and Review
- The Normal Curve & Continuous Probability Distributions: Help and Review
- The Mathematics of Voting: Help and Review
- The Mathematics of Apportionment: Help and Review
- Graph Theory: Help and Review
- Operations with Basic Algebraic Expressions
- Conics in Algebra
- Algebraic Concepts of Groups & Sets
- Notation, Sequences & Series
- Matrices and Determinants in Algebra
- Fractions, Decimals & Mixed Numbers
- Approaches to Math Word Problems
- Performing Basic Arithmetic
- Number Line & the Coordinate Graph