Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Elementary Algebra
Topic: Exponents and Polynomials
Subtopic: Polynomial Operations I - Simplify, Add, & Subtract

Overview

Polynomials are algebraic expressions that (usually) contain several terms such as x5-2x4+5x3+6x-9. Remember when you were in elementary school and you were just learning about numbers? You learned to add and subtract, later multiply, and then the dreaded long divide. Well, that is what we are going to do here except we will be performing these operations with polynomial expressions not plain numbers. So put your algebra hats on and get your pencils warmed up, because we are going to embark on a "polynomic" adventure!

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 6.3.1 Understand the definition of a polynomial
• 6.3.2 Evaluate a polynomial for a given value of a variable
• 6.3.3 Add or subtract two or more polynomials and simplify by collecting like terms
• 6.3.4 Recognize when two polynomials are "opposites" of one another
• 6.3.5 Find the "opposite" of a given polynomial
• 6.3.6 Determine the degree of a term (both single and multi-variable terms)
• 6.3.7 Determine the degree of a polynomial (both single and multi-variable polynomials)
• 6.3.8 Write a polynomial in standard descending order (both single and multi-variable polynomials)

Terminology

Terms you should be able to define: coefficient, variable, exponent, term, polynomial, single-variable vs. multi-variable polynomial, opposite, opposite of a polynomial, degree of a term, degree of a polynomial, standard descending order (SDO)

Text Notes

Although your textbook may stick to single variable polynomials at this point, we will begin to discuss multi-variable polynomials in class now.