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:
- 6.2.1 Understand the definition of a polynomial
- 6.2.2 Evaluate a polynomial for a given value of a variable
- 6.2.3 Add or subtract two or more polynomials and simplify by collecting like terms
- 6.2.4 Determine the degree of a term (both single and multi-variable terms)
- 6.2.5 Determine the degree of a polynomial (both single and multi-variable polynomials)
- 6.2.6 Write a polynomial in standard descending order (both single and multi-variable polynomials)
Terminology
Define: coefficient, variable, exponent, term, polynomial, single-variable vs. multi-variable polynomial, degree of a term, degree of a polynomial, standard descending order (SDO)
Text Notes
Text:
Intro & Inter Algebra for CS 3ed by Blitzer, sect. 5.1
- This section contains lots of important new terminology plus basic operations like combining like terms.
- pg 326 Pay attention to the important term "the opposite of a polynomial".
- This text sticks to single variable polynomials until section 5.4 but we will begin to discuss them in class now.