# Ch 31: HiSET Mathematics: Polynomials

### About This Chapter

## HiSET Mathematics: Polynomials - Chapter Summary

Our professional instructors let you in on some tricks and methods for working with polynomials in our instructional video lessons. You can also read the transcripts that reinforce the material so you are prepared for the types of questions you'll face on the exam, like:

- Adding, subtracting and multiplying polynomials
- Using operations with polynomials in multiple variables
- Dividing polynomials with long division and synthetic division
- Remainder and factor theorems
- Using the rational zeros theorem and synthetic division to find rational zeros
- The fundamental theorem of algebra

### Objectives of the HiSET Mathematics: Polynomials Chapter

The HiSET Math exam assesses your understanding and application of key functions of polynomials. The concepts in this chapter are part of the Algebraic Concepts portion of the exam, which makes up 45% of the entire math test.

All of the questions on the exam are multiple-choice, so be sure to take advantage of our multiple-choice quizzes at the end of every lesson.

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

Adding, subtracting and multiplying polynomials are, basically, the same as adding, subtracting and multiplying numbers. They only difference is that we have a pesky variable to worry about, but this video will show you that's no problem, so no worries! This method has worked for many of my students, and I think it will work for you, too!

### 2. Operations with Polynomials in Several Variables

In this video lesson, you will learn how to handle and work with polynomials that have more than one variable. This is important because in math you sometimes have to work with several variables at the same time.

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

Arithmetic long division and polynomial long division are very similar. Yes, it's a long process, but once you have the rhythm you will get every problem correct!

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

Synthetic division is a 'short-cut' way of dividing a polynomial by a monomial. You still need to know long division, sorry, but this method is way fun when you're dividing by a monomial!

### 5. 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.

### 6. Finding Rational Zeros Using the Rational Zeros Theorem & Synthetic Division

After completing this lesson, you will know what the rational zeros theorem says. You will also know how to apply this theorem to find zeros of polynomial functions.

### 7. Fundamental Theorem of Algebra: Explanation and Example

In this lesson, you will learn what the Fundamental Theorem of Algebra says. You will also learn how to apply this theorem in determining solutions of polynomial functions.

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### Other Chapters

Other chapters within the HiSET Mathematics: Prep and Practice course

- HiSET Mathematics: Mathematical Reasoning
- HiSET Mathematics: Properties of Real Numbers
- HiSET Mathematics: Fractions
- HiSET Mathematics: Decimals and Percents
- HiSET Mathematics: Ratios and Proportions
- HiSET Mathematics: Vector Operations
- HiSET Mathematics: Matrices and Determinants
- HiSET Mathematics: Exponents and Exponential Expressions
- HiSET Mathematics: Absolute Value Problems
- HiSET Mathematics: Rational Expressions
- HiSET Mathematics: Radical Expressions
- HiSET Mathematics: Imaginary and Complex Numbers
- HiSET Mathematics: Measurements and Conversions
- HiSET Mathematics: Foundations of Geometry
- HiSET Mathematics: Introduction to Geometric Figures
- HiSET Mathematics: Properties of Triangles
- HiSET Mathematics: Triangle Theorems and Proofs
- HiSET Mathematics: Parallel Lines and Polygons
- HiSET Mathematics: Quadrilaterals
- HiSET Mathematics: Circular Arcs and Circles
- HiSET Mathematics: Geometric Solids
- HiSET Mathematics: Summarizing Data
- HiSET Mathematics: Probability
- HiSET Mathematics: Probability Distributions
- HiSET Mathematics: Sampling
- HiSET Mathematics: Regression and Correlation
- HiSET Mathematics: Algebraic Expressions
- HiSET Mathematics: Linear Equations
- HiSET Mathematics: Inequalities
- HiSET Mathematics: Quadratic Equations
- HiSET Mathematics: Functions
- HiSET Mathematics Flashcards