# Ch 12: Algebra II - Polynomials: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other high school algebra II work.
- Identify the polynomials concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our high school algebra II tutoring solution will benefit any student who is trying to learn polynomials and earn better grades. This resource can help students including those who:

- Struggle with understanding basic polynomial graphs, basic transformations, quartics and quintics, Pascal's Triangle, the binomial theorem or any other polynomials topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves failing or close to failing their polynomials unit
- Cope with ADD or ADHD
- Want to get ahead in high school algebra II
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors:**We make learning about polynomials simple and fun.**Cost Efficient:**For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality:**Unlike a live algebra II tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about polynomials on the go!**Learn at Your Pace:**You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning Objectives

- Evaluate polynomials in function notation.
- Graph polynomial functions.
- Perform basic transformations on polynomial graphs.
- Graph cubics, quatrics, quintics and more.
- Add, subtract and multiply polynomials.
- Understand how to use Pascal's triangle.
- Become familiar with the binomial expressions used in the binomial theorem.
- Divide polynomials using long division and synthetic division.
- Perform operations using polynomials in several variables.

### 1. How to Evaluate a Polynomial in Function Notation

A polynomial is an algebraic expression that has more than one term and function notation is the way a function is written. In this lesson, explore how to evaluate or solve a polynomial in function notation.

### 2. Understanding Basic Polynomial Graphs

Understanding basic polynomial graphs requires knowing about their degrees and leading coefficients. Learn more about the implications of exponents and leading coefficients in polynomial graphs. Discover also how turning points are determined in graphing polynomials.

### 3. Basic Transformations of Polynomial Graphs

Polynomial graphs can be transformed in four basic ways: up and down, left and right, pinching and stretching, and flipping. Learn the definitions of polynomial functions and parent functions, and also how to analyze basic transformations of polynomial graphs.

### 4. How to Graph Cubics, Quartics, Quintics and Beyond

Following the proper steps, the basic principles of graphing can be applied to cubics, quartics, quintics, and other polynomial functions. Learn more about basic graphing principles for polynomial functions, the importance of local maximums and minimums, and sketching for class on a graph through a detailed practice test question.

### 5. How to Add, Subtract and Multiply Polynomials

Polynomials can be added, subtracted, and multiplied similarly to regular numbers once the variables have been organized. Learn the steps required to apply the principles of addition, subtraction, and multiplication to polynomials through a series of example problems.

### 6. Pascal's Triangle: Definition and Use with Polynomials

Pascal's triangle is a number pattern that identifies the coefficients of polynomial expansions. Learn the definition of Pascal's triangle and explore examples of its polynomial uses.

### 7. The Binomial Theorem: Defining Expressions

The binomial theorem is a mathematical formula used to expand two-term expressions raised to any exponent. Explore this explanation defining what binomial theorem is, why binomial theorem is used, and examples of how to find the leading coefficient and exponents for each term.

### 8. How to Divide Polynomials with Long Division

Polynomials can be divided using long division by dividing the first terms, multiplying the quotient by the divisor, subtracting it from the dividend, and continuously repeating the steps. Learn more about the steps for dividing polynomials with long division and why it is necessary to repeat the steps to complete the operation.

### 9. How to Use Synthetic Division to Divide Polynomials

Synthetic division is a shortened form of dividing polynomials by monomials that is shorter than using long division. Explore several examples of the synthetic division of polynomials and follow the correct order of steps to arrive at much simpler expressions.

### 10. Dividing Polynomials with Long and Synthetic Division: Practice Problems

Polynomials can be divided using both long and synthetic division, and so it is important to be comfortable using both. Learn the steps of both long and synthetic division of polynomials and use them to solve practice problems.

### 11. Operations with Polynomials in Several Variables

Operations with polynomials in several variables are easy to work out with practice. Explore the topic of solving a polynomial by isolating a variable.

### Earning College Credit

Did you know… We have over 220 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Other Chapters

Other chapters within the High School Algebra II: Tutoring Solution course

- Algebra II - Basic Arithmetic Review: Tutoring Solution
- Algebra II - Algebraic Expressions and Equations Review: Tutoring Solution
- Algebra II - Real Numbers: Tutoring Solution
- Algebra II - Complex and Imaginary Numbers Review: Tutoring Solution
- Algebra II - Exponents and Exponential Expressions Review: Tutoring Solution
- Algebra II - Properties of Functions Review: Tutoring Solution
- Algebra II - Linear Equations Review: Tutoring Solution
- Algebra II - Systems of Linear Equations: Tutoring Solution
- Algebra II - Inequalities Review: Tutoring Solution
- Algebra II - Matrices and Determinants: Tutoring Solution
- Algebra II - Absolute Value Review: Tutoring Solution
- Algebra II - Factoring: Tutoring Solution
- Algebra II - Graphing and Factoring Quadratic Equations Review: Tutoring Solution
- Algebra II - Rational Expressions: Tutoring Solution
- Algebra II - Graphing and Functions: Tutoring Solution
- Algebra II - Roots and Radical Expressions Review: Tutoring Solution
- Algebra II - Quadratic Equations: Tutoring Solution
- Algebra II - Exponential and Logarithmic Functions: Tutoring Solution
- Algebra II - Conic Sections: Tutoring Solution
- Algebra II - Sequences and Series: Tutoring Solution
- Algebra II - Sets: Tutoring Solution
- Algebra II - Combinatorics: Tutoring Solution
- Algebra II - Calculations, Ratios, Percent & Proportions Review: Tutoring Solution
- Algebra II - Statistics: Tutoring Solution
- Algebra II - Trigonometry: Tutoring Solution