# 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

A cubic equation is an equation with a third-degree term as its highest ordered term. Learn about the definition and examples of cubic equations, and explore cubic equations in algebra, as well as cubic equation applications in real life.

### 2. How to Solve Perfectly Cubed Equations

In mathematics, multiplying the same number three times yields a perfect cube. Learn how to solve perfectly cubed equations and review the formulas, difference of cubes, and sum of cubes to understand how to work equations for perfect cubes.

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

A perfect cube is a number that results when the same number is multiplied three times, but not all cubes are perfect. Learn how to solve cubic equations that are not perfectly cubed, explore the rational roots theorem, and find the first and other two roots.

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

In algebra, factoring out the greatest common factor is one method of solving cubic equations. Learn what the greatest common factor method is and when it can be used to solve a cubic equation, and practice with an example problem.

### 5. Grouping to Factor Cubic Equations

In mathematics, cubic equations have a polynomial of degree three, and they are factored using different techniques. Learn about the method of grouping to factor cubic equations, explore how to separate an equation's terms, and remove each group's largest common factor, to solve cubic equations.

### 6. Solving Cubic Equations with Integers

Cubic equations, which are polynomial equations with a third-degree term as its highest-ordered term, can be solved by using the rational roots test and polynomial division. Learn about the definition of a cubic equation, how to use the rational roots test to solve for the first root, and the process of using polynomial division for determining the other two solutions.

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

Radical equations can be solved after changing them into linear or quadratic equations. Learn how to solve radical equations by removing the radical and changing them into linear or quadratic equations.

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

In mathematics, a number's square root is the value that produces the number when the value is multiplied by itself, such as 2 is the square root of 4, since 2 x 2 produces 4. Explore how to square both sides of an equation twice, and solve example equations with square roots.

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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