About This Chapter
How It Works:
- Find the lesson within this chapter that corresponds to what you're studying in the Polynomial Functions chapter of your textbook.
- Watch fun videos that cover the polynomial function concepts you need to learn or review.
- Complete the quiz after watching each video lesson 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.
You'll learn all of the algebra topics covered in the textbook chapter, including:
- Adding, subtracting and multiplying polynomials
- Using the difference of two squares
- Dividing polynomials
- Factoring polynomials
- Finding rational zeros
- Using the irrational conjugate theorem and the fundamental theorem
- What Descartes' rule of signs is
- Graphing polynomial functions
- Using the location principle to identify zeros
- Modeling with polynomial functions
Big Ideas Math is a registered trademark of Larson Texts, 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. Analyzing Graphs of Polynomial Functions
This lesson will explain the graph of a polynomial function by identifying properties including end behavior, real and non-real zeros, odd and even degree, and relative maxima or minima. We will then sketch a graph using this information.
4. 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!
5. Binomials: Difference of Two Squares
Sometimes a difficult calculation can be simplified and a complicated math expression can be made smaller with factoring formulas. In this lesson we explore one of the factoring formulas called the difference of squares.
6. Perfect Square Binomial: Definition & Explanation
Learn what sets perfect square binomials apart from other trinomials in the math world. You will also learn an easy method to identify them along with a simple procedure to factor them.
7. 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.
8. 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!
9. 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.
10. Factoring Polynomial Expressions
When it comes to factoring polynomials, there are several methods to choose from depending on what kind of polynomial you are looking at. Watch this video lesson to learn how to identify and use the appropriate method.
11. Binomials: Sum and Difference of Two Cubes
Math derivations often benefit by writing expressions in different forms. Factoring is a common strategy. In this lesson we show how to factor the sum and difference of cubes.
12. 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.
13. 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.
14. Irrational Conjugate Theorem: Definition & Example
Irrational numbers lend themselves well to the study of polynomials. This lesson will explain how and why this is by defining the irrational conjugates theorem and showing how we can use it to determine various characteristics of a polynomial.
15. 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.
16. Descartes's Rule of Signs: Definition & Example
Finding the roots of a polynomial is a common task in math and science applications. In this lesson, we use a method called Descartes's Rule of Signs to predict the number of roots we expect to find.
17. Complex Conjugate: Numbers, Functions & Examples
After completing this lesson, you will be able to describe and define complex conjugates. You will also be able to write complex conjugates and use them appropriately to solve problems.
18. 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.
19. Using X-Intercepts to Graph Polynomial Functions
Graphing polynomials may seem daunting but when you can pinpoint where the function will cross or touch the x-axis, it's much easier. Learn how to find the x-intercepts of a given function and use them to sketch an accurate graph. Practice predicting what the graph should look like.
20. Using the Location Principle to Identify Zeros of Polynomial Functions
In this lesson, we will look at polynomial functions and their zeros. We will look at real world and mathematical examples to define and discuss how to use the location principle to approximate zeros of polynomial functions.
21. Modeling with Polynomial Functions
Modeling real-world phenomena with a function is an extremely useful tool to have at our disposal. This lesson will explain how to model a given set of data points with polynomial functions using the method of finite differences.
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Other chapters within the Big Ideas Math Algebra 2: Online Textbook Help course
- Big Ideas Math Algebra 2 - Chapter 1: Linear Functions
- Big Ideas Math Algebra 2 - Chapter 2: Quadratic Functions
- Big Ideas Math Algebra 2 - Chapter 3: Quadratic Equations and Complex Numbers
- Big Ideas Math Algebra 2 - Chapter 5: Rational Exponents and Radical Functions
- Big Ideas Math Algebra 2 - Chapter 6: Exponential and Logarithmic Functions
- Big Ideas Math Algebra 2 - Chapter 7: Rational Functions
- Big Ideas Math Algebra 2 - Chapter 8: Sequences and Series
- Big Ideas Math Algebra 2 - Chapter 9: Trigonometric Ratios and Functions
- Big Ideas Math Algebra 2 - Chapter 10: Probability
- Big Ideas Math Algebra 2 - Chapter 11: Data Analysis and Statistics