# Ch 22: OAE Middle Grades Math: Monomials & Polynomials

### About This Chapter

## OAE Middle Grades Math: Monomials & Polynomials - Chapter Summary

Use the short video lessons in this chapter to get reacquainted with monomials and polynomials as you get ready to take the OAE Middle Grades Mathematics assessment. After watching the lessons, you will have the knowledge necessary to tackle the following on the exam:

- Defining monomials and polynomials
- Adding, subtracting and multiplying polynomials
- Evaluating a polynomial in a function notation
- Understanding polynomial graphs and their basic transformations
- Defining Pascal's triangle and using it with polynomials
- Analyzing binomial theorem
- Dividing polynomials with long division

The instructors in this chapter present their video lessons in a comprehensive, yet engaging fashion. You'll have access to the definitions and methods you need to understand and solve monomials and polynomials on the exam, while having the chance to absorb the materials in a relaxed learning environment.

### Objectives of the OAE Middle Grades Math: Monomials & Polynomials Chapter

The OAE Middle Grades Mathematics assessment gauges your readiness to teach math in the middle grades classroom and secure a subject-specific teaching license in Ohio. The topics covered in this OAE Middle Grades Math: Monomials & Polynomials chapter are found in the algebra and functions section of the test, which constitutes approximately 33% of the entire exam. You can watch video lessons and review text transcripts to refresh your knowledge of these topics before taking self-assessment quizzes and a chapter exam to strengthen that knowledge.

The assessment is made up of all multiple-choice questions that are based on specific test competencies. Many of the questions are be accompanied by a graph, diagram or illustration to help you conceptualize and solve a problem. Following each question are four answers. You will be asked to choose one of the four as the best response to the question posed.

### 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 Ohio Assessments for Educators - Middle Grades Mathematics (030): Practice & Study Guide course

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