# Ch 16: Higher-Degree Polynomial Functions in Trigonometry: Help and Review

### About This Chapter

## Who's it for?

Anyone who needs help learning or mastering high school trigonometry material will benefit from taking this course. There is no faster or easier way to learn high school trigonometry. Among those who would benefit are:

- Students who have fallen behind in understanding how to factor and solve higher-degree polynomial functions
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about higher-degree polynomial functions
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources

## How it works:

- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Higher-Degree Polynomial Functions in Trigonometry chapter exam.

## Why it works:

**Study Efficiently**: Skip what you know, review what you don't.**Retain What You Learn**: Engaging animations and real-life examples make topics easy to grasp.**Be Ready on Test Day**: Use the Higher-Degree Polynomial Functions in Trigonometry chapter exam to be prepared.**Get Extra Support**: Ask our subject-matter experts any higher-degree polynomial functions question. They're here to help!**Study With Flexibility**: Watch videos on any web-ready device.

## Students will review:

In this course, you'll learn the answers to questions including:

- How can I solve polynomials of a degree greater than or equal to three?
- How do I add, subtract and multiply polynomials?
- What is quadratic form?
- How can I divide polynomials with long and synthetic division?
- How do I apply the remainder and factor theorems?
- What is the rational zeros theorem?
- What is the fundamental theorem of algebra?

### 1. 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.

### 2. Factoring Polynomials Using Quadratic Form: Steps, Rules & Examples

One of the best methods for factoring polynomials of a higher degree is using the quadratic form. Discover the steps and rules of how to change expressions into the quadratic form through examples provided in this lesson.

### 3. How to Divide Polynomials with Long Division

Polynomials can be divided using long division by dividing the first terms, multiplying the quotient by the divisor, subtracting it from the dividend, and continuously repeating the steps. Learn more about the steps for dividing polynomials with long division and why it is necessary to repeat the steps to complete the operation.

### 4. How to Use Synthetic Division to Divide Polynomials

Synthetic division is a shortened form of dividing polynomials by monomials that is shorter than using long division. Explore several examples of the synthetic division of polynomials and follow the correct order of steps to arrive at much simpler expressions.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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.

### Earning College Credit

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### Other Chapters

Other chapters within the High School Trigonometry: Help and Review course

- Real Numbers - Types and Properties: Help and Review
- Working with Linear Equations in Trigonometry: Help and Review
- Working with Inequalities in Trigonometry: Help and Review
- Absolute Value Equations in Trigonometry: Help and Review
- Working with Complex Numbers in Trigonometry: Help and Review
- Systems of Linear Equations in Trigonometry: Help and Review
- Mathematical Modeling in Trigonometry: Help and Review
- Introduction to Quadratics in Trigonometry: Help and Review
- Working with Quadratic Functions in Trigonometry: Help and Review
- Coordinate Geometry Review: Help and Review
- Functions for Trigonometry: Help and Review
- Understanding Function Operations in Trigonometry: Help and Review
- Graph Symmetry in Trigonometry: Help and Review
- Graphing with Functions in Trigonometry: Help and Review
- Basic Polynomial Functions in Trigonometry: Help and Review
- Rational Functions in Trigonometry: Help and Review
- Trig - Rational Expressions & Function Graphs: Help & Review
- Exponential & Logarithmic Functions in Trigonometry: Help and Review
- Trigonometric Functions: Help and Review
- Geometry in Trigonometry: Help and Review
- Triangle Trigonometry: Help and Review
- Working with Trigonometric Graphs: Help and Review
- Trigonometric Equations: Help and Review
- Working with Trigonometric Identities: Help and Review
- Applications of Trigonometry: Help and Review
- Analytic Geometry & Conic Sections in Trigonometry: Help and Review
- Vectors, Matrices & Determinants in Trigonometry: Help and Review
- Polar Coordinates & Parameterizations: Help and Review
- Circular Arcs, Circles & Angles: Help and Review
- TASC Math: Trigonometry