About This Chapter
Polynomial Functions Basics - Chapter Summary and Learning Objectives
Now that you're familiar with functions, use this chapter to get a better idea of how components of polynomial expressions, such as the leading coefficient and degree, can be used to determine the behavior of their graphs. You can even learn some time-saving shortcuts to help you raise these expressions to a power. By the time you finish watching the video lessons in this chapter, you should be able to do the following:
- Graph first- and higher-degree polynomial functions
- Determine a polynomial function's positive and negative intervals
- Describe the short and long run behavior of a polynomial
- Expand a binomial using Pascal's triangle and the binomial theorem
|Terminology of Polynomial Functions||Learn to identify a polynomial function's leading coefficient, leading term and degree.|
|How to Evaluate a Polynomial in Function Notation||Explore the processes involved in using function notation to evaluate a polynomial.|
|Understanding Basic Polynomial Graphs||Learn how to graph first-degree polynomial functions. Explore methods for graphing polynomials written in factored form.|
|Finding Intervals of Polynomial Functions||Determine the positive and negative intervals of a polynomial function with known roots.|
|Short Run & Long Run Behavior of Polynomials: Definition & Examples||Differentiate between polynomials' short run and long run behavior. Provide examples of each.|
|How to Graph Cubics, Quartics, Quintics and Beyond||Learn how to find the x- and y-intercepts and plot points for the graphs of higher-degree polynomials.|
|Pascal's Triangle: Definition and Use with Polynomials||Explore the uses of Pascal's triangle to work with polynomials.|
|The Binomial Theorem: Defining Expressions||Examine the uses of the binomial theorem to define expressions.|
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. 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. Finding Intervals of Polynomial Functions
Watch this video lesson to learn how you can find the intervals of a polynomial function. Also learn how to find out whether each interval is negative or positive.
5. Short Run & Long Run Behavior of Polynomials: Definition & Examples
Watch this video lesson to learn how you can use the graph of a polynomial to help you explain the polynomial function. Learn how to explain the behavior of the polynomial at the origin and at the far ends.
6. 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!
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. 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 Remedial Precalculus course
- Working with Linear Equations
- Working With Inequalities
- Absolute Value Equations
- Working with Complex Numbers
- Systems of Linear Equations
- Mathematical Modeling
- Introduction to Quadratics
- Working with Quadratic Functions
- Geometry Basics for Precalculus
- Functions: Basics for Precalculus
- Understanding Function Operations
- Graph Symmetry
- Graphing with Functions
- Rate of Change
- Higher-Degree Polynomial Functions
- Rational Functions & Difference Quotients
- Rational Expressions and Function Graphs
- Exponential Functions & Logarithmic Functions
- Using Trigonometric Functions
- Trigonometric Graphs
- Solving Trigonometric Equations
- Trigonometric Identities
- Trigonometric Applications
- Graphing Piecewise Functions
- Vectors, Matrices and Determinants
- Mathematical Sequences and Series
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations
- Sets in Algebra