# Ch 25: MEGA Middle School Math: Monomials & Polynomials

### About This Chapter

## MEGA Middle School Math: Monomials & Polynomials - Chapter Summary

Get ready to take the MEGA Middle School Education Mathematics exam. This chapter includes a series of lesson videos that have been assembled to help you solve mathematical problems with monomials and polynomials. In the videos, our expert instructors explain the processes used to:

- Add, subtract, multiply and divide polynomials
- Evaluate polynomials in function notation
- Understand how to use and perform basic transformations on polynomial graphs
- Use Pascal's triangle and the binomial theorem
- Complete operations with polynomials in several variables

For a further review of these topics, scan the lesson transcripts that will also help you identify important concepts. If you come up with any questions about these lessons, be sure to ask our instructors for clarification using the teacher tabs. Before moving on, test your skills by taking the lesson quizzes and the practice chapter exam to ensure you are ready for related questions on the Missouri Educator Gateway Assessments (MEGA) Middle School Education Mathematics exam.

### MEGA Middle School Math: Monomials & Polynomials Chapter Objectives

Before individuals can become certified middle-grades math teachers in the state of Missouri they must score at least a 220 on the MEGA Middle School Education Mathematics exam. In order to do this, they must perform well on a computerized exam that features 80-multiple-choice-questions. Two hours and 30 minutes are allowed for completion. This chapter has been assembled to help you study for some of the questions about monomials and polynomials in the Algebra and Functions content domain which makes up 36% of the exam.

### 1. What Are Monomials & Polynomials?

Watch this video lesson to learn how coefficients and variables combine to form monomials and polynomials. You'll also find out how the exponent determines the degree of polynomials.

### 2. 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!

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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!

### 9. 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!

### 10. Dividing Polynomials with Long and Synthetic Division: Practice Problems

Let's look at some more polynomial division problems. We will use long division and synthetic division, but this time we will have a couple of more involved problems. So, get out some paper and a pencil and let's begin!

### 11. 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.

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### Other Chapters

Other chapters within the MEGA Middle School Mathematics: Practice & Study Guide course

- MEGA Middle School Math: Basic Arithmetic Operations
- MEGA Middle School Math: Solving Word Problems
- MEGA Middle School Math: Properties of Numbers
- MEGA Middle School Math: Estimating & Rounding
- MEGA Middle School Math: Number Theory
- MEGA Middle School Math: Roots & Radical Expressions
- MEGA Middle School Math: Exponents & Exponential Expressions
- MEGA Middle School Math: Scientific Notation
- MEGA Middle School Math: Simplifying Whole Number Expressions
- MEGA Middle School Math: Integers
- MEGA Middle School Math: Rational Numbers
- MEGA Middle School Math: Introduction to Fractions
- MEGA Middle School Math: Operations with Fractions
- MEGA Middle School Math: Introduction to Decimals
- MEGA Middle School Math: Operations with Decimals
- MEGA Middle School Math: Percents
- MEGA Middle School Math: Money & Consumer Math
- MEGA Middle School Math: Number Patterns & Sequences
- MEGA Middle School Math: Properties of Functions
- MEGA Middle School Math: Graphing Functions
- MEGA Middle School Math: Negative Numbers
- MEGA Middle School Math: Absolute Value
- MEGA Middle School Math: Inequalities
- MEGA Middle School Math: Factoring
- MEGA Middle School Math: Writing Algebraic Expressions
- MEGA Middle School Math: Basic Algebraic Expressions
- MEGA Middle School Math: Algebraic Distribution
- MEGA Middle School Math: Solving One-Step Equations
- MEGA Middle School Math: Solving Two-Step Equations
- MEGA Middle School Math: Simplifying Rational Expressions
- MEGA Middle School Math: The Coordinate Graph
- MEGA Middle School Math: Linear Equations
- MEGA Middle School Math: Systems of Linear Equations
- MEGA Middle School Math: Rates, Ratios & Proportions
- MEGA Middle School Math: Measurements
- MEGA Middle School Math: Perimeter & Area
- MEGA Middle School Math: Polyhedrons & Geometric Solids
- MEGA Middle School Math: Symmetry, Similarity & Congruence
- MEGA Middle School Math: Properties of Lines
- MEGA Middle School Math: Angles
- MEGA Middle School Math: Triangles
- MEGA Middle School Math: Triangle Theorems & Proofs
- MEGA Middle School Math: Similar Polygons
- MEGA Middle School Math: The Pythagorean Theorem
- MEGA Middle School Math: Quadrilaterals
- MEGA Middle School Math: Circles
- MEGA Middle School Math: Circular Arcs & Measurement
- MEGA Middle School Math: Transformations
- MEGA Middle School Math: Data & Graphs
- MEGA Middle School Math: Statistics
- MEGA Middle School Math: Data Collection
- MEGA Middle School Math: Samples & Populations
- MEGA Middle School Math: Probability
- MEGA Middle School Math: Sets
- MEGA Middle School Mathematics Flashcards