About This Chapter
Algebra II: Polynomials Overview - Chapter Summary
High school students need to read and understand a great deal of information both before they graduate and as they move on in college or the professional world. This chapter provides students with focused training on polynomials.
Instead of an endless chapter of information, the chapter has been divided into short, individualized lessons. Students have the option to review all of the lessons in order, but they can also pick and choose lesson topics in which they need the most assistance. The chapter menu provides a list of all lessons available, and since each lesson is only focused on a single topic, students can easily find what they need. After completing this chapter, students will be ready to:
- Understand basic polynomial graphs and their basic transformations
- Evaluate a polynomial in function notation
- Define Pascal's Triangle and use it with polynomials
- Use the binomial theorem to expand binomial expressions
- Explain the remainder theorem and factor theorem
- Outline the process of using the rational roots theorem
1. Understanding Basic Polynomial Graphs
This lesson will cover understanding basic polynomial graphs. The lesson focuses on how exponents and leading coefficients alter the behavior of the graphs.
2. How to Evaluate a Polynomial in Function Notation
This lesson will review how to evaluate polynomials in function notation. Along with an analogy to explain the process, examples will be given and worked during the lesson.
3. Basic Transformations of Polynomial Graphs
The basic transformations for a graph are movement up and down, left and right, pinched or stretched graphs, and flipped graphs. This lesson will review how to accomplish each of these transformations.
4. Pascal's Triangle: Definition and Use with Polynomials
Pascal's Triangle is defined and discussed briefly. Following the introduction to the triangle, its use in expanding polynomial powers is elaborated with examples.
5. The Binomial Theorem: Defining Expressions
In this lesson, students will learn the binomial theorem and get practice using the theorem to expand binomial expressions. The theorem is broken down into its parts and then reconstructed.
6. Remainder Theorem & Factor Theorem: Definition & Examples
In this lesson, you will learn about the remainder theorem and the factor theorem. You will also learn how to use these theorems to find remainders and factors of polynomials.
7. How to Use the Rational Roots Theorem: Process & Examples
When it comes to solving polynomials, it can sometimes be easier to begin with a list of possible solutions to try. This video lesson tells you how to form a list of possible solutions by using the rational roots theorem.
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Other chapters within the High School Algebra II: Homeschool Curriculum course
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations Review
- Algebra II: Absolute Value Review
- Algebra II: Inequalities Review
- Algebra II: Working with Real Numbers
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Factoring Review
- Algebra II: Quadratic Equations Review
- Algebra II: Graphing and Factoring Quadratic Equations Review
- Algebra II: Complex and Imaginary Numbers
- Algebra II: Rational Expressions Review
- Algebra II: Polynomials Review
- Algebra II: Graphing Polynomial Functions
- Algebra II: Conic Sections
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Sequences & Series
- Algebra II: Combinatorics Review
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistical Analysis
- Algebra II: Trigonometry Review
- Algebra II: Trigonometry Overview
- Algebra II: Assignments & Projects
- Homeschool Resources for High School Algebra II