# Ch 49: 8th Grade Math: Algebraic Monomials & Polynomials

### About This Chapter

## 8th Grade Math: Algebraic Monomials & Polynomials - Chapter Summary

Take your 8th grader's classroom training to the next level with these lessons on monomials and polynomials. The video lessons in this chapter use graphics and engaging narration to help your students perform operations with monomials, evaluate polynomials and use graphs. Reinforce their knowledge of critical concepts by having them complete the self-assessment quizzes and chapter exam.

## Chapter Lessons and Objectives

Lesson | Objective |
---|---|

Monomials & Polynomials | Students see definitions for monomials and polynomials and learn how a degree of a polynomial is found. |

How to Add and Subtract Monomials | Lesson allows students to practice adding and subtracting monomials. |

How to Multiply and Divide Monomials | Instructors outline the steps needed to multiply and divide polynomials and provide opportunities for students to practice. |

Square and Cube Roots Of Monomials | Students practice finding the square and cube roots of monomials. |

How to Evaluate a Polynomial in Function Notation | Lesson uses examples to describe the process of evaluating polynomials in function notation. |

Understanding Basic Polynomial Graphs | Video provides details on the components of polynomial graphs. |

Basic Transformations of Polynomial Graphs | Instructors show students how to identify different transformations on a graph. |

How to Graph Cubics, Quartics, Quintics and Beyond | Students learn the steps for graphing quintics, cubics and quartics. |

How to Add, Subtract and Multiply Polynomials | Lesson provides the steps for performing these operations with polynomials. |

Pascal's Triangle: Definition and Use with Polynomials | Samples are used in this chapter to outline the process of using Pascal's triangle. |

The Binomial Theorem: Defining Expressions | Students learn about the expressions used in the binomial theorem. |

How to Divide Polynomials with Long Division | Lesson shows how to use long division to divide polynomials. |

How to Use Synthetic Division to Divide Polynomials | Video shows the process of dividing polynomials with synthetic division. |

Dividing Polynomials with Long and Synthetic Division: Practice Problems | Students apply the skills they've acquired in previous lessons to divide polynomials. |

Operations with Polynomials in Several Variables | Lesson teaches students how to evaluate polynomials in several variables. |

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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!

### 5. 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.

### 6. 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.

### 7. 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!

### 8. 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!

### 9. 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!

### 10. 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.

### 11. Transformations in Math Project Ideas

This asset offers multiple group and individual projects designed to allow students to showcase their summative knowledge of transformations in Math. The projects engage students in creative learning and expression.

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### Other Chapters

Other chapters within the 8th Grade Math: Practice & Review course

- 8th Grade Math: Basic Arithmetic Operations
- 8th Grade Math: Divisibility
- 8th Grade Math: Number Properties
- 8th Grade Math: Number Theory
- 8th Grade Math: Factoring
- 8th Grade Math: Estimation and Rounding
- 8th Grade Math: Whole Numbers
- 8th Grade Math: Simplifying Whole Number Expressions
- 8th Grade Math: Negative Numbers
- 8th Grade Math: Absolute Value
- 8th Grade Math: Integers
- 8th Grade Math: Rational Numbers
- 8th Grade Math: Inequalities
- 8th Grade Math: Introduction to Decimals
- 8th Grade Math: Operations with Decimals
- 8th Grade Math: Introduction to Fractions
- 8th Grade Math: Operations with Fractions
- 8th Grade Math: Percents
- 8th Grade Math: Exponents & Exponential Expressions
- 8th Grade Math: Roots & Radical Expressions
- 8th Grade Math: Basic Algebraic Expressions
- 8th Grade Math: Algebraic Distribution
- 8th Grade Math: Simplifying & Solving Rational Expressions
- 8th Grade Math: The Coordinate Graph
- 8th Grade Math: Linear Equations
- 8th Grade Math: Systems of Linear Equations
- 8th Grade Math: Properties of Functions
- 8th Grade Math: Graphing Functions
- 8th Grade Math: Solving Math Word Problems
- 8th Grade Math: Introduction to Geometric Figures
- 8th Grade Math: Triangles in Geometry
- 8th Grade Math: Quadrilaterals in Geometry
- 8th Grade Math: Circles in Geometry
- 8th Grade Math: Circular Arcs & Measurement in Geometry
- 8th Grade Math: Polyhedrons and Geometric Solids
- 8th Grade Math: Symmetry, Similarity & Congruence in Geometry
- 8th Grade Math: Triangle Theorems and Proofs in Geometry
- 8th Grade Math: Similar Polygons in Geometry
- 8th Grade Math: The Pythagorean Theorem in Geometry
- 8th Grade Math: Units of Measurement
- 8th Grade Math: Measuring Perimeter & Area
- 8th Grade Math: Data & Graphs
- 8th Grade Math: Probability
- 8th Grade Math: Statistics
- 8th Grade Math: Rates, Ratios & Proportions
- 8th Grade Math: Consumer Math
- 8th Grade Math: Number Sequences
- 8th Grade Math: Sets & Subsets