About This Chapter
Explorations in Core Math Algebra 2 Chapter 3: Polynomial Functions- Chapter Summary and Learning Objectives
In this chapter, you'll learn about polynomial functions and how to solve equations with polynomial functions. Our lively lessons and multiple-choice quizzes offer solid information, so, by the time you have completed this chapter, you should be able to do the following:
- Distinguish the difference between polynomials, binomials and quadratics
- How to graph polynomial functions
- Understand what Pascal's triangle is
- Learn about the theorems involved with polynomial functions
|What are Polynomials, Binomials, and Quadratics?||Compare and contrast polynomials, binomials and quadratics.|
|How to Add, Subtract and Multiply Polynomials||Understand how to apply basic math to polynomials.|
|Special Product: Definition & Formula||Learn about what a binomial is and how to multiply them.|
|Pascal's Triangle: Definition and Use with Polynomials||Review what Pascal's Triangle is.|
|How to Use the Binomial Theorem to Expand a Binomial||Apply knowledge of the binomial theorem to binomials.|
|Remainder Theorem & Factor Theorem: Definition & Examples||Take a look at the remainder and factor theorem.|
|Dividing Polynomials with Long and Synthetic Division: Practice Problems||Analyze different division problems involving polynomials.|
|Factoring Polynomial Expressions||See how to properly factor polynomials.|
|Graphing Factorable Polynomial Functions||Explore polynomial functions and how to graph them.|
|Finding Rational Zeros Using the Rational Zeros Theorem & Synthetic Division||Discover the rational zero theorem.|
|Fundamental Theorem of Algebra: Explanation and Example||Apply the fundamental theorem in solving polynomial functions.|
|How Values Affect the Behavior of Polynomial Functions||Determine the characteristics of even and odd functions.|
|Basic Transformations of Polynomial Graphs||Understand how transformations of graphs affect polynomial graphs.|
|Modeling with Polynomial Functions||Find out how to write polynomial function for sets of points.|
1. What are Polynomials, Binomials, and Quadratics?
Polynomials, binomials, and quadratics refer to the number of terms an expression has in math. Study the definition and the three restrictions of polynomials, as well as the definitions of binomials and quadratics.
2. How to Add, Subtract and Multiply Polynomials
Polynomials can be added, subtracted, and multiplied similarly to regular numbers once the variables have been organized. Learn the steps required to apply the principles of addition, subtraction, and multiplication to polynomials through a series of example problems.
3. Special Product: Definition & Formula
Special products are the result of binomials being multiplied, or simplified further, and can be solved with ease using the FOIL method: first, outer, inner, last. Learn how to use these steps, and master binomial formulas by practicing below.
4. Pascal's Triangle: Definition and Use with Polynomials
Pascal's triangle is a number pattern that identifies the coefficients of polynomial expansions. Learn the definition of Pascal's triangle and explore examples of its polynomial uses.
5. How to Use the Binomial Theorem to Expand a Binomial
The binomial theorem can be used to determine the expanded form of a binomial multiplied by itself numerous times. Learn about the binomial theorem, understand the formula, explore Pascal's triangle, and learn how to expand a binomial.
6. Remainder Theorem & Factor Theorem: Definition & Examples
In algebra, the remainder theorem is a formula used to find the remainder when dividing a polynomial by a linear polynomial, while the factor theorem links a polynomial's zeros and factors. Learn what this means by exploring the definitions and examples of both theorems.
7. Dividing Polynomials with Long and Synthetic Division: Practice Problems
Polynomials can be divided using both long and synthetic division, and so it is important to be comfortable using both. Learn the steps of both long and synthetic division of polynomials and use them to solve practice problems.
8. Factoring Polynomial Expressions
In algebra, it is important to know how to factor polynomial expressions. Learn some different methods of factoring polynomial expressions, including factoring quadratics, using the greatest common factor, and grouping, as well as how and when to use these methods.
9. Graphing Factorable Polynomial Functions
Some polynomials can be factored. If a polynomial function is factorable then you can find the graph of the function by using the zeros and the end behavior.
10. Finding Rational Zeros Using the Rational Zeros Theorem & Synthetic Division
A rational zero is a number that can be expressed as a fraction of two numbers, while an irrational zero has a decimal that is infinite and non-repeating. Learn how to use the rational zeros theorem and synthetic division, and explore the definitions and work examples to recognize rational zeros when they appear in polynomial functions.
11. Fundamental Theorem of Algebra: Explanation and Example
The Fundamental Theorem of Algebra states that every polynomial function includes a minimum of one complex zero. Using an analogy based on bank fees, explore an explanation and examples of how to apply the theorem, and learn about imaginary, repeated, and complex solutions.
12. How Values Affect the Behavior of Polynomial Functions
A polynomial function is a function that involves only the same category integer in an equation. Learn how specific values can determine a function's end behavior.
13. Basic Transformations of Polynomial Graphs
Polynomial graphs can be transformed in four basic ways: up and down, left and right, pinching and stretching, and flipping. Learn the definitions of polynomial functions and parent functions, and also how to analyze basic transformations of polynomial graphs.
14. 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 Explorations in Core Math - Algebra 2: Online Textbook Help course
- Explorations in Core Math Algebra 2 Chapter 1: Foundations for Functions
- Explorations in Core Math Algebra 2 Chapter 2: Quadratic Functions
- Explorations in Core Math Algebra 2 Chapter 4: Exponential and Logarithmic Functions
- Explorations in Core Math Algebra 2 Chapter 5: Rational and Radical Functions
- Explorations in Core Math Algebra 2 Chapter 6: Properties and Attributes of Functions
- Explorations in Core Math Algebra 2 Chapter 7: Probability
- Explorations in Core Math Algebra 2 Chapter 8: Data Analysis and Statistics
- Explorations in Core Math Algebra 2 Chapter 9: Sequences and Series
- Explorations in Core Math Algebra 2 Chapter 10: Trigonometric Functions
- Explorations in Core Math Algebra 2 Chapter 11: Trigonometric Graphs and Identities
- Explorations in Core Math Algebra 2 Chapter 12: Conic Sections