Learning Guide Unit 3 PDF

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Learning Guide Unit 3 Site: Course: Book: Printed by: Date:

University of the People MATH 1201 College Algebra - AY2021T2 Learning Guide Unit 3 Abdulrahman Kailani Wednesday, 2 December 2020, 5:55 PM

Description Learning Guide Unit 3

Table of contents Overview Introduction Reading Assignment Discussion Assignment Learning Journal Self-Quiz Graded Quiz Checklist

Overview

Unit 3: Polynomials

Topics: Graphs The Factor Theorem and the Remainder Theorem Complex Zeroes and the Fundamental Theorem of Algebra

Learning Objectives: By the end of this Unit, you will be able to: 1. Develop a polynomial or rational function to model a real-world situation. 2. Discuss roots of polynomials given information about them. 3. Reect on the concept of polynomial and rational functions.

Tasks: Peer assess Unit 2 Written Assignment Read the Learning Guide and Reading Assignments Participate in the Discussion Assignment (post, comment, and rate in the Discussion Forum) Complete an entry in the Learning Journal Take the Self-Quiz Take the Graded Quiz

Introduction

Further critical concepts in the course are addressed here. You will nd it very helpful to memorize the graphs of the basic functions (especially parabolas and square roots. A new type of number, a “complex number” is introduced, allowing us to nd more solutions to equations. The complex numbers allow the polynomial equations to be solved with great harmony. In this way, the degree of the polynomial determines the number of solutions. They also allow the annoying fact that negative numbers do not have square roots to be corrected, but paying the price of terms that widen the space of numbers. The numbered line lled by the real numbers extends to the numbered plane of the complex numbers. On the other hand, the ease that we have nowadays to get the function graphs through software gives us the visualization of the important behavior of the polynomial functions.

Reading Assignment Abramson, J. (2017). Algebra and trigonometry . OpenStax, TX: Rice University Read the following sections in Chapter 5: Section 5.2 Power Functions and Polynomial Functions Section 5.3 Graphs of Polynomial Functions Section 5.4 Dividing Polynomials Section 5.5 Zeros of Polynomial Functions Section 5.6 Rational Functions You should attempt the exercises in the book as indicated below. These exercises help to establish an understanding of the concepts involved. If necessary, reread the examples and exercises solved in the book. The answers are at the end of the book. Section 5.2 exercises: 1, 11, 21, 31, 41, 51, 67, 69 Section 5.3 exercises: 1, 11, 21, 31, 41, 51, 61, 71, 75, 77 Section 5.4 exercises: 1, 11, 21, 31, 41, 45, 51, 61, 65, 67, 71 Section 5.5 exercises: 1, 11, 21, 31, 41, 51, 57, 59, 61, 71, 77 Section 5.6 exercises: 1, 11, 21, 31, 41, 51, 61, 71, 81. You are allowed to use the book and other resources to answer the problems. You are welcome to ask about these in the Course Forum.

Optional Video Resources Access this online resource for additional instruction and practice. Mathispower4u. (2012, June 12). Ex: Find key information about a given polynomial function [Video le]. Retrieved from

Ex: Find Key Information about a Given…

Mathispower4u. (2012, June 11). Summary of end behavior or long run behavior of polynomial functions [Video le]. Retrieved from

Summary of End Behavior or Long Run …

Mathispower4u. (2012, June 12). Turning points and x intercepts of a polynomial function [Video le]. Retrieved from

Turning Points and X Intercepts of a Po…

Mathispower4u. (2012, June 12). Ex: Determine the least possible degree of a polynomial from the graph [Video le]. Retrieved from

Ex: Determine the Least Possible Degr…

Mathispower4u. (2012, June 12). Ex: Determine the least possible degree of a polynomial from the graph [Video le]. Retrieved from

Ex: Determine the Least Possible Degr…

 Mathispower4u. (2013, June 19). Intermediate Value Theorem [Video le]. Retrieved from

Intermediate Value Theorem

Mathispower4u. (2011, October 9). Ex 1: Divide a trinomial by a binomial using long division [Video le]. Retrieved from

Ex 1: Divide a Trinomial by a Binomial …

Mathispower4u. (2011, October 9). Ex 4: Divide a polynomial by a binomial using synthetic division [Video le]. Retrieved from

Ex 4: Divide a Polynomial by a Binomial…

Mathispower4u. (2013, May 20). Real zeros, factors, and graphs of polynomial functions [Video le]. Retrieved from

Real Zeros, Factors, and Graphs of Pol…

Mathispower4u. (2013, May 20). Polynomial function - Complex factorization theorem [Video le]. Retrieved from

(New Version Available) Polynomial Fu…

Mathispower4u. (2012, April 20). Ex 1: Find the zeros of a polynomial function - Integer zeros [Video le]. Retrieved from

Ex 1: Find the Zeros of a Polynomial Fu…

Mathispower4u. (2012, April 20). Ex 2: Find the zeros of a polynomial function - Real rational zeros [Video le]. Retrieved from

Ex 2: Find the Zeros of a Polynomial Fu…

Mathispower4u. (2012, April 20). Ex 3: Find the zeros of a polynomial function with irrational zeros [Video le]. Retrieved from

Ex 3: Find the Zeros of a Polynomial Fu…

Mathispower4u. (2011, December 8). Ex 1: Graphing rational functions [Video le]. Retrieved from

Ex 1: Graphing Rational Functions

 Mathispower4u. (2012, June 20). Ex 1: Find the equation of rational function from a graph with a hole [Video le]. Retrieved from

Ex 1: Find the Equation of Rational Fun…

Mathispower4u. (2011, March 18). Determining vertical and horizontal asymptotes of rational functions [Video le]. Retrieved from

Determining Vertical and Horizontal As…

Mathispower4u. (2012, June 20). Ex: Find the intercepts, asymptotes, and hole of a rational function [Video le]. Retrieved from

Ex: Find the Intercepts, Asymptotes, an…

Discussion Assignment Polynomial and rational functions can be used to model a wide variety of phenomena of science, technology, and everyday life. Choose one of these sectors and give an example of a polynomial or rational function modeling a situation in that sector. [Hint: see the examples and exercises in the book.] Go to www.desmos.com/calculator, write your equation, or function, and develop your explanation using the properties of graphs. Your Discussion should be a minimum of 250 words in length and not more than 750 words.

Learning Journal

Reect on the concept of polynomial and rational functions. What concepts (only the names) did you need to accommodate these concepts in your mind? What are the simplest polynomial and rational function you can imagine? In your day to day, is there any occurring fact that can be interpreted as polynomial and rational functions? What strategy are you using to get the graph of polynomial and rational functions? The Learning Journal entry should be a minimum of 400 words and not more than 750 words.

Self-Quiz

The Self-Quiz gives you an opportunity to self-assess your knowledge of what you have learned so far.

The results of the Self-Quiz do not count towards your nal grade, but the quiz is an important part of the University’s learning process and it is expected that you will take it to ensure understanding of the materials presented. Reviewing and analyzing your results will help you perform better on future Graded Quizzes and the Final Exam.

Please access the Self-Quiz on the main course homepage; it will be listed inside the Unit.

Graded Quiz

The Graded Quiz will test your knowledge of all the materials learned thus far. The results of the quiz will count towards your nal grade. Please access the Graded Quiz on the main course homepage; it will be listed inside the Unit. After you click on it, the quiz’s introduction will inform you of any time or attempt limits in place. Good luck!

Checklist

Peer assess Unit 2 Written Assignment

Read the Learning Guide and Reading Assignments

Participate in the Discussion Assignment (post, comment, and rate in the Discussion Forum)

Complete an entry in the Learning Journal

Take the Self-Quiz

Take the Graded Quiz

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