Topic: Exponents and Polynomials
Subtopic: Polynomial Operations II - Multiply, FOIL, & Special Products
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:
- 6.3.1 Use the distributive law to multiply a monomial by a polynomial
- 6.3.2 Use FOIL to multiply two binomials
- 6.3.3 Use the horizontal method to multiply two polynomials
- 6.3.4 Use the vertical method to multiply two polynomials
- 6.3.5 Use Pascals Triangle to expand binomials to higher powers
- 6.3.6 Perform multiple operations on polynomials following order or operations as needed
- 6.3.7 Recognize special products and polynomial: difference of squares, binomial squared, perfect squared trinomials
Terminology
Define: distributive law, FOIL, difference of squares, binomial squared, perfect square trinomial (PST), horizontal vs. vertical method of multiplying polynomials, Pascal's Triangle
Text Notes
Text:
Intro & Inter Algebra for CS 3ed by Blitzer, sect. 5.2-5.4
- ch 5.2 begins with basic rules of positive exponents.
- ch 5.2 covers polynomial multiplication including the distributive law (for multiplying a monomial through a polynomial), the horizontal method (for multiplying two polynomials that are each binomials or larger), and the vertical method (similar to the horizontal method but written in a different configuration).
- ch 5.3 covers the very important FOIL method which is a shortcut for multiplying two binomials.
- ch 5.3 has formulas that can be used instead of FOIL for multiplying a difference of squares or for squaring a binomial. I strongly recommend that you memorize these formulas prior to Intermediate Mathematics when we will take the FOILed-out polynomial and backtrack to the ( )( ) form.
- ch 5.3 The text fails to cover using Pascal's triangle here as I believe it should. For an explanation see page 993 and explanatory posts on the main classroom board. A liberal arts math course such as MATH& 107 will delve much deeper into PT.
- ch 5.4 expands the processes in 5.1-5.3 by performing them with multivariate polynomials (polys that contain several variables like x, y, and z's not just x's).