## Understanding Polynomials: A Brief Introduction

The purpose of this lesson is to develop a student foundation for understanding the components of polynomials, including the use of variables, exponents, constants, and mathematical operators. By understanding the basic components of polynomials, students will become prepared for operations among polynomials, similar to what students will have accomplished previously with operations among numbers or linear equations.

#### GED Content Areas

Algebra and Functions

## Adding Polynomials

The purpose of this lesson is for students to understand that the rules for adding polynomials are analogous to the rules for adding integers. Students apply the rules for addition by building upon previous knowledge and understanding of polynomial terms.

#### GED Content Areas

Algebra and Functions

## Subtracting Polynomials

The purpose of this lesson is for students to understand that the rules for subtracting polynomials are analogous to the rules for subtracting integers. Students apply the rules of subtraction by building upon previous knowledge and understanding of polynomial terms.

Understanding polynomial operations is siginificant because it is the first major area outside of the basic two-step, one-variable algebra problems that are traditionally taught to students at the beginning levels in algebra.

The real world often requires that people be able to make sense of multiple variables that are numerous yet related. Understanding the rules of polynomial operations is one way to abstractly model many of those kinds of situations.

#### GED Content Areas

Algebra and Functions

## Multiply Polynomials

The purpose of this lesson is for students to understand that the rules for multiplying polynomials are analogous to the rules for multiplying integers. Students apply the rules for multiplying by building upon previous knowledge and understanding of polynomial terms.

#### GED Content Areas

Algebra and Functions

## Factoring Polynomials

The purpose of this lesson is for students to understand that the rules for factoring polynomials involve the simultaenous satisfaction of a very specific addition and multiplication calculation by using specific parts of the polynomial. This calculation is able to give the inverse result of a multiplication problem, and has direct application to may geometry questions. Finally, factoring a polynomial involves higher-order thinking skills that are helpful and analagous to the type of thinking required int he real world in order to solve complex problems involving more than one variable; particularly in the cases where recursive reasoning is necessary.

#### GED Content Areas

Algebra and Functions