# Ch 25: NES Middle Grades Math: Monomials & Polynomials

### About This Chapter

## NES Middle Grades Math: Monomials and Polynomials - Chapter Summary

Expand your ability to solve problems with monomials and polynomials. This chapter's short videos and quizzes cover topics such as Pascal's triangle, variables, leading coefficients, polynomial and parent functions, and the binomial theorem. Up and down and left and right transformations are also highlighted. The chapter provides information that will assist you with answering test questions on:

- Identifying polynomials and monomials
- Multiplying, subtracting and adding polynomials
- Discussing the necessary steps for evaluating polynomials in function notation
- Working with polynomial graphs
- Understanding the basic types of polynomial transformations
- Using Pascal's triangle with polynomials
- Learning more about the binomial theorem
- Dividing polynomials with long and synthetic division, and completing practice problems
- Solving polynomials that have one variable

Build upon your knowledge of monomials and polynomials through the instruction and guidance of professional educators and math experts. The animated videos are available online 24/7. Navigational video tags and written transcripts can make studying more fun and convenient.

### NES Middle Grades Math: Monomials and Polynomials Chapter Objectives

This chapter and its educational videos can be utilized to help you answer questions on monomials and polynomials when you reach the the *Algebra and Functions* content domain of the NES Middle Grades Math examination. This section of the test is worth 33% of the entire score. There's a four-hour and 15-minute time limit on the overall computer-administered examination, which is composed of 150 multiple-choice questions.

### 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 NES Middle Grades Mathematics (203): Practice & Study Guide course

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