About This Chapter
How it works:
- Identify the lessons in the Prentice Hall Algebra 2 Polynomials and Polynomial Functions chapter with which you need help.
- Find the corresponding video lessons within this companion course chapter.
- Watch fun videos that cover the polynomials and polynomial functions topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.
Students will learn:
- Basic polynomial graphs
- Use of rational and complex zeros to write polynomial equations
- How to divide polynomials with long division
- Factoring of polynomials using quadratic form
- Use of the Rational Zeros Theorem and synthetic division to find rational zeros
- How to calculate permutations
- Pascal's Triangle
Prentice Hall Algebra 2 is a registered trademark of Pearson Education, Inc., which is not affiliated with Study.com.
1. Terminology of Polynomial Functions
After watching this video lesson, you will be able to understand and use the words associated with polynomial functions like a pro. You will see words, such as leading coefficient, and you will immediately know what it is referring to.
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. 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.
4. Using Rational & Complex Zeros to Write Polynomial Equations
In this lesson, you will learn how to write a polynomial function from its given zeros. You will learn how to follow a process that converts zeros into factors and then factors into polynomial functions.
5. 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!
6. 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!
7. 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!
8. Polynomial Functions: Properties and Factoring
Everything from projectile motion to trigonometric functions can be described by polynomials. Review factoring, polynomials and quadratic functions in this lesson.
9. Factoring By Grouping: Steps, Verification & Examples
How do you factor an expression if all the terms don't share a common factor? Grouping! In this lesson, we'll learn how to use grouping to help factor expressions.
10. Factoring Polynomials Using Quadratic Form: Steps, Rules & Examples
Factoring a polynomial of degree 4 or higher can be a difficult task. However, some polynomials of higher degree can be written in quadratic form, and the techniques used to factor quadratic functions can be utilized.
11. Finding Rational Zeros Using the Rational Zeros Theorem & Synthetic Division
After completing this lesson, you will know what the rational zeros theorem says. You will also know how to apply this theorem to find zeros of polynomial functions.
12. Fundamental Theorem of Algebra: Explanation and Example
In this lesson, you will learn what the Fundamental Theorem of Algebra says. You will also learn how to apply this theorem in determining solutions of polynomial functions.
13. What Is a Factorial?
Maybe it's because I'm a math teacher, but when I watched the Olympics I found myself thinking about how many different ways the swimmers could have finished the race. In this video, you'll learn the answer to this question, why it's important and how it lead to the invention of the mathematical operation called the factorial.
14. How to Calculate a Permutation
A permutation is a method used to calculate the total outcomes of a situation where order is important. In this lesson, John will use permutations to help him organize the cards in his poker hand and order a pizza.
15. Math Combinations: Formula and Example Problems
Combinations are an arrangement of objects where order does not matter. In this lesson, the coach of the Wildcats basketball team uses combinations to help his team prepare for the upcoming season.
16. 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.
17. 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.
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Other chapters within the Prentice Hall Algebra 2: Online Textbook Help course
- Prentice Hall Algebra 2 Chapter 1: Tools of Algebra
- Prentice Hall Algebra 2 Chapter 2: Functions, Equations, and Graphs
- Prentice Hall Algebra 2 Chapter 3: Linear Systems
- Prentice Hall Algebra 2 Chapter 4: Matrices
- Prentice Hall Algebra 2 Chapter 5: Quadratic Equations and Functions
- Prentice Hall Algebra 2 Chapter 7: Radical Functions and Rational Exponents
- Prentice Hall Algebra 2 Chapter 8: Exponential and Logarithmic Functions
- Prentice Hall Algebra 2 Chapter 9: Rational Functions
- Prentice Hall Algebra 2 Chapter 10: Quadratic Relations and Conic Sections
- Prentice Hall Algebra 2 Chapter 11: Sequences and Series
- Prentice Hall Algebra 2 Chapter 12: Probability and Statistics
- Prentice Hall Algebra 2 Chapter 13: Periodic Functions and Trigonometry
- Prentice Hall Algebra 2 Chapter 14: Trigonometric Identities and Equations