About This Chapter
Factoring & Graphing Polynomials - Chapter Summary
Get practice factoring and graphing polynomials with this convenient online math chapter. As you work through these short lessons at your own pace, you'll evaluate polynomial function properties and theorems, as well as the methods that are used to graph and factor polynomials. When you're finished with the chapter, you'll be equipped to:
- Recognize the properties of polynomial functions
- Understand basic polynomial graphs
- Use long division to divide polynomials and quadratic form to factor polynomials
- Explain the remainder theorem, factor theorem and fundamental theorem of algebra
- Graph cubics, quartics and quintics
- Factor polynomials over complex numbers
The chapter is available at any time that fits your schedule, and you can access it using your computer or smartphone. Be sure to take the accompanying self-assessment quizzes to check your understanding of the polynomial terms, formulas and theorems. If you get stuck or need any extra help, our instructors are available to answer your questions.
1. 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.
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. 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!
4. 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.
5. 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.
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. 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.
8. Factorization of Polynomials Over Complex Numbers
In this lesson we show show how to factor polynomials when the factors contain complex numbers. Using examples, we show how this is an extension of cases where the factors are purely real.
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Other chapters within the HSC Mathematics: Exam Prep & Syllabus course
- Mathematical Proofs & Reasoning
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Logarithmic & Exponential Functions
- Calculating Trigonometric Functions
- Understanding Inverse Functions
- Roots & Coefficients of Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards