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 III - FOIL

Overview

Continuing our work with polynomials, in this lesson we focus on multiplication of polynomials including the very important FOIL method. As you are doing the FOIL problems think about how you might work this process backwards (going from the answer trinomial back to the product of two binomials) because that ("factoring") is exactly where we start in an Intermediate Algebra course!

Objectives

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

• 6.5.1 Use FOIL to multiply two binomials
• 6.5.2 Use the horizontal or vertical method to multiply two polynomials
• 6.5.3 Use Pascals Triangle to expand binomials to higher powers
• 6.5.4 Perform multiple operations on polynomials following order or operations as needed
• 6.5.5 Perform operations on single variable polynomials and multi-variable polynomials

Terminology

Terms you should be able to define: FOIL, horizontal vs. vertical method of multiplying polynomials, Pascal's Triangle

Text Notes

Your textbook may or may not cover Pascal's Triangle. Pascal's Triangle is useful in algebra and statistics and has a wealth of historical interest. In class we will cover the basics of using Pascal's Triangle to expand binomials to a power, such as (x+y)5. A college level liberal arts mathematics course will delve deeper particularly in the area of statistics, probability, and combinatorics.