# Ch 4: Expanding Polynomials

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### About This Chapter

## Expanding Polynomials - Chapter Summary

This chapter's lessons look at polynomials, binomials and quadratics. You'll learn about polynomial graphs and adding, subtracting and multiplying polynomials. Other lessons explore methods of dividing polynomials.

These lessons introduce you to the binomial theorem and its uses and also help you find out how to multiply binomials with FOIL and the area method. After watching all these lessons, you'll be able to:

- Evaluate a polynomial using function notation
- Use basic polynomial graphs
- Graph cubics, quartics and quintics
- Divide polynomials with long division and synthetic division
- Perform operations with polynomials in several variables
- Define expressions and expand a binomial with the binomial theorem
- Use FOIL and the area method

These brief video lessons are led by experienced instructors. The lessons are followed by multiple-choice quizzes that let you test your knowledge. The jump feature in the timeline allows you to quickly go back and find major concepts in each video that you need to review. Each lesson is also available as a written transcript with key terms highlighted.

### 1. What are Polynomials, Binomials, and Quadratics?

What do polynomials, binomials, and quadratics have in common? What are their differences? How can you identify each of them? Watch this video lesson to find the answers.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. 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!

### 6. 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!

### 7. 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!

### 8. 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!

### 9. 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!

### 10. 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.

### 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 Use the Binomial Theorem to Expand a Binomial

In this video lesson, you will see what the binomial theorem has in common with Pascal's triangle. Learn how you can use Pascal's triangle to help you to easily expand a binomial.

### 13. Multiplying Binomials Using FOIL and the Area Method

From the distributive property, to FOIL, to the area model, to happy faces and claws, there are many different ways to learn how to multiply binomials. In this lesson, you'll learn how to use all of them and get to pick which one you like the most.

### 14. Multiplying Binomials Using FOIL & the Area Method: Practice Problems

There are a few mistakes that are easy to make when multiplying binomials with FOIL and also a few ways to complicate problems like this, so why not make sure you're brushed up on your skills? You'll also learn a shortcut and how to use the area method to multiply even bigger polynomials.

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### Other Chapters

Other chapters within the Accuplacer College Level Math Test: Practice & Study Guide course

- Operations with Basic Algebraic Expressions
- Arithmetic with Rational Expressions
- Factoring in Algebra
- Manipulating Roots
- Working with Exponents & Exponential Expressions
- Solving & Graphing Linear Equations
- Quadratic Equations
- Calculating & Graphing Inequalities
- Solving Systems of Linear Equations
- Geometric Angles & Shapes
- Conics in Algebra
- Algebraic Concepts of Groups & Sets
- Graphs of Algebraic Functions
- Complex and Imaginary Numbers
- Notation, Sequences & Series
- Matrices and Determinants in Algebra
- Combinatorics
- Fractions, Decimals & Mixed Numbers
- Approaches to Math Word Problems
- Understanding Exponential & Logarithmic Functions
- Trigonometric Functions & Equations