About This Chapter
Algebra II: Polynomials - Chapter Summary
As you move into advanced mathematical graphing, you will begin to study polynomials and related concepts. These lessons provide an introduction about polynomials, including graphing procedures, steps for performing operations, and more. All of our lessons are online and can be accessed through your own user dashboard. You no longer have to worry about keeping your study materials organized, because we keep everything for you in one, easy-to-navigate location. Use your favorite Internet-ready device to review our materials, or print out any of our available worksheets to enhance your notes. By the time you finish this algebra II chapter, you should have the ability to do the following:
- Describe how to use function notation for evaluating polynomials
- Identify basic polynomial graphs
- Analyze polynomial graphs and basic transformations
- Check out steps for graphing quintics, quartics, cubics, and more
- Define ways to multiply, subtract, or add polynomials
- Examine how to use Pascal's Triangle with polynomials
- Point out expressions of the binomial theorem
- Offer long division examples for dividing polynomials
- Review synthetic division
- Show differences with synthetic and long division techniques
- Determine how to perform polynomial operations with multiple variables
1. 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.
2. 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.
3. 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.
4. 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!
5. 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!
6. 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.
7. 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.
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. Remainder Theorem & Factor Theorem: Definition & Examples
In this lesson, you will learn about the remainder theorem and the factor theorem. You will also learn how to use these theorems to find remainders and factors of polynomials.
12. 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 Algebra II: High School course
- Algebra II: Real Numbers
- Algebra II: Complex and Imaginary Numbers Review
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Properties of Functions Review
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations
- Algebra II: Inequalities Review
- Algebra II: Absolute Value Review
- Algebra II: Graphing and Factoring Quadratic Equations Review
- Algebra II: Quadratic Equations
- Algebra II: Factoring
- Algebra II: Rational Expressions
- Algebra II: Graphing and Functions
- Algebra II: Conic Sections
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Sequences & Series
- Algebra II: Combinatorics
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistics
- Algebra II: Trigonometry
- Homeschool Resources for High School Algebra II
- Algebra II: Assignments & Projects