Back To Course

SAT Prep: Help and Review38 chapters | 326 lessons

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Log in here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*David Liano*

After completing this lesson, you will be able to state the Zero Product Property and apply it to real numbers and algebraic expressions. You will also be able to solve equations using the Zero Product Property.

What is the **zero product property**? Let *A* and *B* be real numbers or algebraic expressions. If the product of *A* and *B* is zero, then *A* = 0 or *B* = 0. It is also possible that both *A* and *B* are zero. An **algebraic expression** is any expression involving variables. For instance, *y*, *xy*, *x* + 3, and *x*^2 + 9 are all examples of algebraic expressions.

It is important to understand that the product of any number multiplied by zero equals zero. Let's say that Melanie have a lemonade stand and is selling glasses of lemonade at a price of $0.25 each. There is unexpected rain, so no customers stop by the stand. In other words, Melanie sell zero glasses of lemonade. How much money did she bring in? She collected no money, so her sales are $0.25 x 0 = $0.00.

There are many standard forms for equations. It is usually based on the type of equation. For this lesson, it will be helpful if you express equations so that zero is the value of one side of the equation:

*expression* = 0

Say that you have *x*^2 + 2*x* = 24. If we want one side of the equation to equal zero, we can subtract 24 from both sides. This gives us *x*^2 + 2*x* - 24 = 0.

Take the equation 7*x* = 0. Based on the zero product property, either 7 = 0 or *x* = 0. It is known that 7 cannot equal zero, therefore, *x* must equal zero.

Now look at the equation *xyz* = 0. Even though there are three variables, you can separate the expression on the left side of the equation into two expressions. You can have (*xy*)*z* = 0. You now have two expressions: *xy* and *z*. Based on the zero product property, either *xy* = 0 or *z* = 0. Using the commutative property, we can separate the original expression into any combination of two expressions, but the zero product property will still apply.

The zero product property is very handy when finding solutions to quadratic equations that can be factored.

Take the equation *y*^2 + 5*y* = 0. If we factor out a *y*, you get *y*(*y* + 5) = 0. The two expressions here are *y* and *y* + 5. At least one of the expressions must equal zero. In other words, *y* = 0 or *y* + 5 = 0. You need to solve each equation for *y*. So, you have:

*y* = 0

or

*y* + 5 = 0; *y* = -5

The possible values of *y* are 0 and -5.

Go back to the quadratic equation: *x*^2 + 2*x* - 24 = 0. If you factor this quadratic equation, you get (*x* + 6)(*x* - 4) = 0. You now have the product of two expressions that equal zero. The two expressions or factors are (*x* + 6) and (*x* - 4). By the zero product property, at least one of the expressions equals zero. You need to solve each equation for *x*:

*x* + 6 = 0; *x* = -6

or

*x* - 4 = 0; *x* = 4

The possible values of *x* are -6 and 4.

Do not over think the zero product property. Zero of anything gives you nothing except an expression or numerical symbol that represents zero. If the product of two expressions equals zero, then at least one of the expressions must be zero.

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Log in here for access

Did you know… We have over 160 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

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
21 in chapter 26 of the course:

Back To Course

SAT Prep: Help and Review38 chapters | 326 lessons

- How to Divide Complex Numbers 6:40
- How to Add, Subtract and Multiply Complex Numbers 5:59
- Solve Problems Using Percents 7:50
- Percents: Definition, Application & Examples 6:20
- How to Find the Least Common Multiple 5:37
- How to Find the Prime Factorization of a Number 5:36
- How to Find the Greatest Common Factor 4:56
- Scientific Notation: Definition and Examples 6:49
- Solving Radical Equations: Steps and Examples 6:48
- Simplify Square Roots of Quotients 4:49
- Simplifying Square Roots of Powers in Radical Expressions 3:51
- Roots and Powers of Algebraic Expressions 5:00
- Radicands and Radical Expressions 4:29
- What is PEMDAS? - Definition, Rule & Examples 9:07
- What Are Compatible Numbers? - Definition & Examples 5:49
- What Are Prime Numbers? - Definition & Examples 5:03
- What Are Relatively Prime Numbers? - Examples & Calculations 4:38
- What are Roman Numerals? - Number Conversion & Chart 3:39
- What Are Triangular Numbers? - Definition, Formula & Examples 5:47
- What is Value in Math? - Definition & Explanation 3:34
- Zero Product Property: Definition & Examples 4:11
- Go to Math - Numbers and Operations: Help and Review

- SIE Exam Study Guide
- Indiana Real Estate Broker Exam Study Guide
- Grammar & Sentence Structure Lesson Plans
- Foundations of Science Lesson Plans
- Career, Life, & Technical Skills Lesson Plans
- Business Costs, Taxes & Inventory Valuations
- Using Math for Financial Analysis
- Assessments in Health Education Programs
- Governmental Health Regulations
- Understanding Health Education Programs
- AFOQT Prep Product Comparison
- ACT Prep Product Comparison
- CGAP Prep Product Comparison
- CPCE Prep Product Comparison
- CCXP Prep Product Comparison
- CNE Prep Product Comparison
- IAAP CAP Prep Product Comparison

- What is Deadlock? - Definition, Examples & Avoidance
- El Hombre que se Convirtio en Perro: Author, Summary & Theme
- Achilles in The Iliad: Character Analysis & Description
- A Wrinkle in Time Chapter 5 Summary
- Roald Dahl Project Ideas
- Media Literacy Activities for High School
- Letter M Activities
- Quiz & Worksheet - Shang Dynasty Religion & Culture
- Quiz & Worksheet - Alternative Assessment Types
- Quiz & Worksheet - Population Composition
- Quiz & Worksheet - Minimalist Painters
- Analytical & Non-Euclidean Geometry Flashcards
- Flashcards - Measurement & Experimental Design
- Rubrics | Rubric Definition and Types
- Common Core Math Standards - What is Common Core Math?

- English Grammar: Help & Review
- OSAT Middle Level Social Studies (CEOE) (027): Practice & Study Guide
- High School Physics: Homeschool Curriculum
- MEGA Earth Science: Practice & Study Guide
- ASSET Numerical Skills Test: Practice & Study Guide
- American Novelists - 9th Grade: Homeschool Curriculum
- GRE Quantitative Reasoning - Probability and Statistics: Tutoring Solution
- Quiz & Worksheet - What are Differentiation Strategies?
- Quiz & Worksheet - Role of HR Development
- Quiz & Worksheet - Understanding & Describing Roundworms
- Quiz & Worksheet - Cultural Capital
- Quiz & Worksheet - Calculating Real Interest Rates

- Yellow Fever Virus: Structure and Function
- Gratiano in Othello: Character Analysis & Quotes
- How to Pass the CCRN Exam
- Homeschooling in California
- Professional Development Resources for High School Teachers
- How to Pass the Bar Exam
- Writing Prompts for Middle School
- Romeo and Juliet Act 4 Lesson Plan
- New York State Physical Education Standards
- Virginia Real Estate Licensing & Continuing Education
- Homeschooling in Ohio
- Creative Writing Competitions for High School Students

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject