# Ch 20: High School Algebra: Cubic Equations

### About This Chapter

## High School Algebra: Cubic Equations - Chapter Summary and Learning Objectives

Lessons in this chapter begin by introducing you to the practical applications of cubic equations. Our instructor also outlines methods for simplifying these equations and removing radicals so you can solve them with ease. Examples are included in every lesson, as are short multiple-choice quizzes useful for solidifying your understanding of the material. This chapter is designed to teach you how to:

- Solve cubic equations with irrational cube roots
- Solve cubic equations with integers
- Factor cubic equations

Video | Objectives |
---|---|

What is a Cubic Equation? - Definition & Examples | Learn what a cubic equation is and why they're important to algebra and in real life. |

How to Solve Perfectly Cubed Equations | Find out how to solve an equation with two terms that are both perfect cubes. |

How to Solve Equations that are Not Perfectly Cubed | Examine methods for solving a cubic equation with irrational cube roots. |

Using the Greatest Common Factor to Solve Cubic Equations | Practice solving cubic equations in which you can factor out a variable using the greatest common factor. |

Grouping to Factor Cubic Equations | Describe the process of grouping to factor cubic equations. |

Solving Cubic Equations with Integers | Explain how to apply the method of integer factors to solve cubic equations with all integer solutions. |

Changing Radical Equations into Linear or Quadratic Equations | Examine why you would convert an equation containing radicals into either a linear or quadratic equation. Learn how to raise the radical to a power that changes the fractional exponent to 1. |

Squaring Both Sides of an Equation Twice | Learn how to square terms twice in order to get rid of all the radicals in an equation. |

### 1. What is a Cubic Equation? - Definition & Examples

In algebra, you come across various kinds of functions. You start learning about linear functions, and then quadratic functions. Now, though, you come across cubic functions. What are they? Watch this video lesson to find out.

### 2. How to Solve Perfectly Cubed Equations

Watch this video lesson so you can identify perfectly cubed equations. Learn about the formula that helps you factor them and then to solve them. See how easy it is to use these formulas.

### 3. How to Solve Equations that are Not Perfectly Cubed

Watch this video lesson to learn what to do when you have a cubic equation that is not perfectly cubed. Learn an easy method to find all three roots or solutions.

### 4. Using the Greatest Common Factor to Solve Cubic Equations

Watch this video lesson to learn how to identify the cubic equations for which you can factor out the greatest common factor to help you solve them. Learn the steps you need to take to solve them.

### 5. Grouping to Factor Cubic Equations

Factoring a quadratic equation may seem super easy to you now as you step into the world of cubic equations. Watch this video lesson to learn one easy method that you can use to factor some cubic equations.

### 6. Solving Cubic Equations with Integers

Solving quadratic equations is one thing since you have the use of the quadratic formula, but what about solving cubic equations? Watch this video lesson to learn an easy method you can use to help you solve them.

### 7. Changing Radical Equations into Linear or Quadratic Equations

There are all kinds of equations you have to learn how to solve. In this video lesson, you will learn how to remove the radical symbol so you can easily solve equations with radicals in them.

### 8. Squaring Both Sides of an Equation Twice

Okay, so you got the whole solving for x part down. But what will happen if your x is inside a square root? What do you do then? Watch this video lesson to learn what you can do.

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### Other Chapters

Other chapters within the Remedial Algebra I course

- High School Algebra: Basic Arithmetic
- High School Algebra: Solving Math Word Problems
- High School Algebra: Decimals and Fractions
- High School Algebra: Percent Notation
- High School Algebra: Real Numbers
- High School Algebra: Exponents and Exponential Expressions
- High School Algebra: Radical Expressions
- High School Algebra: Algebraic Expressions and Equations
- High School Algebra: Properties of Functions
- High School Algebra: Matrices and Absolute Value
- High School Algebra: Working With Inequalities
- High School Algebra: Properties of Exponents
- High School Algebra: Complex and Imaginary Numbers
- High School Algebra: Algebraic Distribution
- High School Algebra: Linear Equations
- High School Algebra: Factoring
- High School Algebra: Graphing and Factoring Quadratic Equations
- High School Algebra: Properties of Polynomial Functions
- High School Algebra: Rational Expressions
- High School Algebra: Quadratic Equations
- High School Algebra: Measurement and Geometry
- High School Algebra: Calculations, Ratios, Percent & Proportions
- High School Algebra: Data, Statistics, and Probability
- High School Algebra: Well-Known Equations