Learning Guide Unit 3 College Algebra 1201 PDF

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Summary

The course material that you can look into before the course start. It's just something to get you a general view. It's nothing much. The text is from the forum itself....

Description

Learning Guide Unit 3 Overview

Unit 3: Polynomials

Topics:

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Graphs

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The Factor Theorem and the Remainder Theorem

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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. Reflect on the concept of polynomial and rational functions.

Tasks:

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Peer assess Unit 2 Written Assignment

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Read the Learning Guide and Reading Assignments

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

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Complete an entry in the Learning Journal

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Take the Self-Quiz

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Take the Graded Quiz

Introduction

Further critical concepts in the course are addressed here. You will find 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 find 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 filled 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:

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Section 5.2 Power Functions and Polynomial Functions

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Section 5.3 Graphs of Polynomial Functions

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Section 5.4 Dividing Polynomials

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Section 5.5 Zeros of Polynomial Functions

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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 file]. Retrieved from 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 Guide Unit 3 Learning Journal

Reflect 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....