Multiplying & Dividing

Multiplying and Dividing

Site: TBAISD Moodle
Course: Michigan Algebra I Preview 2012
Book: Multiplying & Dividing
Printed by: Guest user
Date: Sunday, July 5, 2020, 03:55 AM

Table of contents

Introduction

Multiplying and dividing functions will require more steps than adding and subtracting functions. While this topic will be covered more thoroughly in the Polynomial Unit, multiplying of linear terms and dividing by a monomial will be discussed here.

The function notation for multiplying and dividing is very similar to adding and subtracting. When multiplying functions, MultiplyingAndDividing1 When dividing two functions, MultiplyingAndDividing2 , where MultiplyingAndDividing3 because division by zero is an undefined operation in mathematics.

Listen

Multiplying

When multiplying a monomial (or one term expression) by a binomial (or two-term expression), the Distributive Property will be used to multiply the two functions.

Example Given Multiplying1 and Multiplying2 , find Multiplying3 .

Step 1. Replace f(x) and g(x) with their equivalent expressions.

Multiplying4

Step 2. Use the Distributive Property to multiply and simplify.

Multiplying5

For a review of the Distributive Property, select the following link:

Distributive Property

Listen


FOIL Method

One method that can be used when multiplying two binomials is the FOIL method. FOIL stands for First, Outer, Inner, and Last. These letters help to remember to multiply each term in the first binomial by each term in the second binomial using the Distributive Property.

Example Given FOIL1 and FOIL2, find FOIL3.

Step 1. Replace f(x) and g(x) with their equivalent expressions.

FOIL4

Step 2. Multiply the First, Outer, Inner, and Last terms of each binomial.

First + Outer + Inner + Last

FOIL5a + FOIL5b + FOIL5c + FOIL5d

Step 3. Simplify the expressions.

FOIL6

For a review of the FOIL method of multiplying, please select the following link:

F+O+I+L Method

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Interactive Activity

To solidify your understanding of multiplying two binomials, select the following link:

Multiplying Binomials

Practice

Multiplying Binomials Worksheet

Answer Key

Multiplying Binomials Answer Key

Dividing

When dividing two functions, Dividing1 , remember that g(x) Dividing2 since division by zero is undefined. To divide a polynomial by a monomial, divide each term of the polynomial by the monomial. Remember to watch the signs of the terms when dividing and that a number divided by itself is one, do not cancel these terms.

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Example 1

Given f(x) = 5x + 35 and g(x) = 5, find Dividing1-1 .

Step 1. Replace f(x) and g(x) with their equivalent expressions.

Dividing1-2

Step 2. Divide each term of the polynomial by the monomial.

Dividing1-3

Step 3. Simplify.

Dividing1-4

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Example 2

Given f(x) = 2x2 + 4x + 10 and g(x) = 2, find Dividing2-1 .

Step 1. Replace f(x) and g(x) with their equivalent expressions.

Dividing2-2

Step 2. Divide each term of the polynomial by the monomial.

Dividing2-3

Step 3. Simplify.

Dividing2-4

Listen

Video Lesson

To learn more on how to multiply and divide functions, please select the following link:

Multiplying and Dividing Functions

Guided Practice

To solidify your understanding of function operations, visit the following link to Holt, Rinehart and Winston Homework Help Online. It provides examples, video tutorials and interactive practice with answers available. The Practice and Problem Solving section has two parts. The first part offers practice with a complete video explanation for the type of problem with just a click of the video icon. The second part offers practice with the solution for each problem only a click of the light bulb away.

Guided Practice

Practice

Multiplying and Dividing Functions Worksheet

Answer Key

Multiplying and Dividing Functions Answer Key

Sources

Embracing Mathematics, Assessment & Technology in High Schools; A Michigan Mathematics & Science Partnership Grant Project

Holt, Rinehart & Winston, "Multiplying and Dividing Functions." http://my.hrw.com/math06_07/nsmedia/lesson_videos/alg2/player.html?contentSrc=7172/7172.xml (accessed 8/10/2010).

Holt, Rinehart & Winston, "Properties and Attributes of Functions." http://my.hrw.com/math06_07/nsmedia/homework_help/alg2/alg2_ch09_04_homeworkhelp.html (accessed 8/18/2010).

Jenkins, "NutshellMath Homework Help: The Distributive Property." http://www.freemathhelp.com/Lessons/Algebra_1_The_Distributive_Property_BB.htm (accessed 07/18/2010).

Kuta Software, www.kutasoftware.com/free.html (accessed 07/19/2010).

Wilcox, Ted. "HotMath: Using the FOIL Method." 2007. http://www.freemathhelp.com/using-foil.html (accessed 07/18/2010).