# Ch 12: Calculating & Graphing Polynomials

### About This Chapter

## Calculating & Graphing Polynomials - Chapter Summary and Learning Objectives

You can explore a wide variety of topics related to polynomials in this comprehensive collection of lessons. Learn all about evaluating, graphing and performing basic functions with polynomials, while gaining a clear understanding of Pascal's Triangle and the Binomial Theorem. Refer to the written lesson transcript anytime that you'd like and take each lesson's short quiz to mark your progress. As you near the end of these lessons, you'll find that you have a solid grasp on the following topics and concepts:

- Polynomials in function notation
- Polynomial graphs and transformations
- Adding, subtracting, multiplying and dividing polynomials
- Long and synthetic division of polynomials

Video | Objective |
---|---|

How to Evaluate a Polynomial in Function Notation | Find out how to substitute values for the variables of functions. |

Understanding Basic Polynomial Graphs | Discover how leading coefficients and exponents can change the behavior of graphs. |

Basic Transformations of Polynomial Graphs | Learn the four types of polynomial graph transformations. |

How to Graph Cubics, Quartics, Quintics and Beyond | Review basic graphs and find out what it means to sketch for class. |

How to Add, Subtract and Multiply Polynomials | Find out the simple method for performing the basic operations with a variable included. |

Pascal's Triangle: Definition and Use with Polynomials | Examine how Pascal's Triangle can help you expand polynomial powers. |

The Binomial Theorem: Defining Expressions | Learn how to expand binomial expressions with this theorem. |

How to Divide Polynomials with Long Division | Examine two easy steps to repeat as often as needed for dividing polynomials with long division. |

How to Use Synthetic Division to Divide Polynomials | When dividing by a monomial, find out how this short-cut can be a fun diversion. |

Dividing Polynomials with Long and Synthetic Division | Let the expert instructor help you review and then guide you through some more complicated examples. |

Operations with Polynomials in Several Variables | Discover the steps for working with polynomials having more than one variable. |

### 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. 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.

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

Other chapters within the Algebra 2 and Trig Textbook course

- Identifying Real Numbers
- Complex Numbers
- Absolute Value Review
- Solving Algebraic Expressions & Equations
- Calculating Rational Expressions
- Working with Linear Equations
- Solving & Graphing Inequalities
- Graphing & Working with Trigonometric Functions
- Graph Symmetry
- Graphing with Functions
- Solving Linear Equations
- Calculating & Simplifying Exponential Expressions
- Square Roots & Radical Expressions
- Quadratic Equations & Formulas
- Factoring & Graphing Quadratic Equations
- Conic Sections: Ellipses, Circles, Hyperbolas & Parabolas
- Vectors, Matrices and Determinants
- Exponential Functions & Logarithmic Functions
- Arithmetic & Geometric Sequences & Series
- Calculating & Presenting Statistics
- Combinatorics & Probability
- Using Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Applications
- Solving Trigonometric Equations
- Trigonometric Identities
- Circles, Angles & Circular Arcs