# Ch 19: Michigan Merit Exam - Math: Polynomial Functions

### About This Chapter

## Michigan Merit Exam - Math: Polynomial Functions - Chapter Summary

If you've been having problems subtracting or dividing polynomials, you can use the video lessons in this chapter to help you. Use our quizzes to test how well you understand how to utilize the remainder theorem. Your study sessions with this chapter will assist you in your ability to answer the questions about the following on exam day:

- Ways to add and perform other operations with polynomial functions
- Variables and polynomials
- Long division with polynomials
- Synthetic division
- Definition of remainder theorem and factor theorem
- Rational zeroes theorem
- Example of the fundamental theorem
- Simple polynomial graphs
- Polynomial grafts and transformations
- Definition of the expressions in a binomial theorem

Please contact our instructors or experts if you have any questions about the lessons. Use the timeline if you need to go to different areas of the videos. You can also review the lessons by reading the video transcripts that contain helpful key terms.

### Michigan Merit Exam - Math: Polynomial Functions Objectives

One of four test components, the Algebra and Functions math section of the Michigan Merit exam could contain questions that will ask you to show your knowledge of how to create different polynomial functions. Once again, this chapter will help you answer that question. The math section of the Michigan Merit Exam includes 25 multiple-choice questions in all.

### 1. 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!

### 2. Operations with Polynomials in Several Variables

In this video lesson, you will learn how to handle and work with polynomials that have more than one variable. This is important because in math you sometimes have to work with several variables at the same time.

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

Synthetic division is a 'short-cut' way of dividing a polynomial by a monomial. You still need to know long division, sorry, but this method is way fun when you're dividing by a monomial!

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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

Other chapters within the Michigan Merit Exam - Math: Test Prep & Practice course

- Michigan Merit Exam - Math: Number Systems & Number Sense
- Michigan Merit Exam - Math: Representations & Relationships
- Michigan Merit Exam - Math: Counting & Probabilistic Reasoning
- Michigan Merit Exam - Math: Using Real & Complex Numbers
- Michigan Merit Exam - Math: Sequences & Iteration
- Michigan Merit Exam - Math: Measurement Units, Calculations & Scales
- Michigan Merit Exam - Math: Understanding Error
- Michigan Merit Exam - Math: Mathematical Reasoning
- Michigan Merit Exam - Math: Language, Laws & Proof of Logic
- Michigan Merit Exam - Math: Using Algebraic Expressions
- Michigan Merit Exam - Math: Properties of Functions
- Michigan Merit Exam - Math: Working with Functions
- Michigan Merit Exam - Math: Lines & Linear Functions
- Michigan Merit Exam - Math: Absolute Values
- Michigan Merit Exam - Math: Inequalities
- Michigan Merit Exam - Math: Exponential & Logarithmic Functions
- Michigan Merit Exam - Math: Quadratic Functions
- Michigan Merit Exam - Math: Power Functions
- Michigan Merit Exam - Math: Rational Functions
- Michigan Merit Exam - Math: Trigonometric Functions
- Michigan Merit Exam - Math: Euclidean & Coordinate Geometry
- Michigan Merit Exam - Math: Triangles & Their Properties
- Michigan Merit Exam - Math: Triangles & Trigonometry
- Michigan Merit Exam - Math: Quadrilaterals & Their Properties
- Michigan Merit Exam - Math: Other Polygons & Their Properties
- Michigan Merit Exam - Math: Circles & Their Properties
- Michigan Merit Exam - Math: Conic Sections & Their Properties
- Michigan Merit Exam - Math: 3D Figures
- Michigan Merit Exam - Math: Comparing Area & Volume Formulas
- Michigan Merit Exam - Math: 2D & 3D Representations
- Michigan Merit Exam - Math: Congruence & Similarity
- Michigan Merit Exam - Math: Transformations & Isometries
- Michigan Merit Exam - Math: Dilations & Isometries
- Michigan Merit Exam - Math: Creating & Interpreting Plots
- Michigan Merit Exam - Math: Measures of Center & Variation
- Michigan Merit Exam - Math: The Normal Distribution
- Michigan Merit Exam - Math: Scatterplots & Correlation
- Michigan Merit Exam - Math: Linear Regression
- Michigan Merit Exam - Math: Data Collection & Analysis
- Michigan Merit Exam - Math: Probability
- Michigan Merit Exam - Math: Application & Representation
- Michigan Merit Exam - Math Flashcards