![more zero product law work common core algebra 1 homework OML Search](https://www.onlinemathlearning.com/image-files/oml-search.png)
![](http://writinghelp.online/777/templates/cheerup/res/banner1.gif)
Zero-Product Property
New york state common core math algebra i, module 4, lesson 5.
Lesson 5 Summary
Zero Product Property
If ab = 0, then a = 0 or b= 0 or a = b = 0 When solving for the variable in a quadratic equation, rewrite the equation as a factored quadratic set equal to zero. Using the zero product property, you know that if one factor is equal to zero, then the product of all factors is equal to zero.
![more zero product law work common core algebra 1 homework Mathway Calculator Widget](https://www.onlinemathlearning.com/image-files/mw-widget-sm.png)
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.
Please enable scripting (or JavaScript) in your web browser, and then reload this page.
Common Core Algebra 1
These interactive lessons use dynamic graphing and guided discovery to strengthen and connect symbolic and visual reasoning. They give the student a hands-on visual exposition of all Common Core Algebra 1 topics, reinforced by adaptive exercises and randomly generated tests. All exercises and tests are checked and graded automatically. Hover the mouse over a link below to see an example from that lesson, or click on a test link to see a concise summary of a group of lessons. Relevant standards are listed after each lesson’s exercises, with a ' (prime) denoting a distinct link. We also provide a course glossary .
The Common Core and other standards cover many algebraic topics before the first actual High School Algebra course. Therefore, students may have already completed many of the lessons and exercises below in an earlier grade, or in a summer preparatory course . If so, those assignments will be treated as already completed in this course also.
Students should have scratch paper available, access to (software or hardware) numeric calculators except during the Arithmetic Review chapter, and other students or a teacher to ask for help when they are stuck. All students are encouraged to both give and receive mathematical explanations with their peers. Please send us your comments, questions and suggestions.
Arithmetic Review (Optional )
Variables, expressions, and simple equations, linear graphs, inequalities, absolute value, and square roots, descriptive statistics, systems of linear equations or inequalities, quadratic expressions, graphs, and equations, the pythagorean theorem, exponential growth and decay.
Zero Product Principle
Anything multiplied by zero is zero.
![more zero product law work common core algebra 1 homework Atoms Practice](https://image2.ck12.org/media/build-20240831065404/images/modality_generic_icons/practice_image.png)
- Assign Practice
- All Modalities
- Assign to Class
- Create Assignment
- Add to Library
- Share with Classes
- Add to FlexBook® Textbook
- Edit Edit View Latest Customize Customize help icon
- PDF Most Devices
- mobi Kindle
- ePub iPad and Android
Notes/Highlights
Color | Highlighted Text | Notes | |
---|---|---|---|
Show More |
Image Attributions
Show hide details, description, learning objectives, difficulty level, date created:, last modified:, other details, concept nodes:, show hide resources.
Zero Product Property
The "Zero Product Property" says that:
If a × b = 0 then a = 0 or b = 0 (or both a=0 and b=0)
It can help us solve equations:
Example: Solve (x−5)(x−3) = 0
The "Zero Product Property" says:
If (x−5)(x−3) = 0 then (x−5) = 0 or (x−3) = 0
Now we just solve each of those:
For (x−5) = 0 we get x = 5
For (x−3) = 0 we get x = 3
And the solutions are:
x = 5 , or x = 3
Here it is on a graph:
Standard Form of an Equation
Sometimes we can solve an equation by putting it into Standard Form and then using the Zero Product Property:
The "Standard Form" of an equation is:
(some expression) = 0
In other words, "= 0" is on the right, and everything else is on the left.
Example: Put x 2 = 7 into Standard Form
x 2 − 7 = 0
Standard Form and the Zero Product Property
So let's try it out:
Example: Solve 5(x+3) = 5x(x+3)
It is tempting to divide by (x+3), but that is dividing by zero when x = −3
So instead we can use "Standard Form":
5(x+3) − 5x(x+3) = 0
Which can be simplified to:
(5−5x)(x+3) = 0
5(1−x)(x+3) = 0
Then the "Zero Product Property" says:
(1−x) = 0, or (x+3) = 0
x = 1 , or x = −3
And another example:
Example: Solve x 3 = 25x
It is tempting to divide by x, but that is dividing by zero when x = 0
So let's use Standard Form and the Zero Product Property.
Bring all to the left hand side:
x 3 − 25x = 0
Factor out x:
x(x 2 − 25) = 0
x 2 − 25 is a difference of squares , and can be factored into (x − 5)(x + 5) :
x(x − 5)(x + 5) = 0
Now we can see three possible ways it could end up as zero:
x = 0 , or x = 5 , or x = −5
- Rating Count
- Price (Ascending)
- Price (Descending)
- Most Recent
Algebra 1 common core
![more zero product law work common core algebra 1 homework Algebra 1 Common Core](https://ecdn.teacherspayteachers.com/thumbuserhome/Algebra-1-Common-Core/8477586.jpg)
Common Core Algebra 1 PROJECTS - BUNDLE PRICE!
![more zero product law work common core algebra 1 homework](https://ecdn.teacherspayteachers.com/thumbuserhome/Math-Byrd-1703934262/7805262.jpg)
Algebra 1 Review Solving Algebraic Expressions Equations Common Core 6.EE.A.2
![more zero product law work common core algebra 1 homework](https://ecdn.teacherspayteachers.com/thumbuserhome/Promoting-Success-1713754012/7515.jpg)
Algebra 1 Common Core Regents Review and Test Prep Bundle
![more zero product law work common core algebra 1 homework](https://ecdn.teacherspayteachers.com/thumbuserhome/Math-With-Nicole-Tomei-1712744913/12029460.jpg)
Common Core Algebra 1 Regents Review Packet
![more zero product law work common core algebra 1 homework](https://ecdn.teacherspayteachers.com/thumbuserhome/Mastering-Math-In-The-Middle-1701114943/2570019.jpg)
Common Core Algebra 1 POSTERS - BUNDLE PRICE!
![more zero product law work common core algebra 1 homework Preview of Statistics Algebra 1 Curriculum Unit 10 Bundle for Common Core](https://ecdn.teacherspayteachers.com/thumbitem/Statistics-Algebra-1-Curriculum-Unit-10-Bundle-for-Common-Core-2714827-1720995033/original-2714827-1.jpg)
Statistics Algebra 1 Curriculum Unit 10 Bundle for Common Core
![more zero product law work common core algebra 1 homework](https://ecdn.teacherspayteachers.com/thumbuserhome/Math-Lion-1721011303/1433604.jpg)
![](http://writinghelp.online/777/templates/cheerup/res/banner1.gif)
Algebra 1 Common Core Standards Checklist and I Can Statements
![more zero product law work common core algebra 1 homework](https://ecdn.teacherspayteachers.com/thumbuserhome/Clevercommoncore-1715859408/645491.jpg)
Algebra 1 Common Core Mastery Tests -- all 13 topics
![more zero product law work common core algebra 1 homework](https://ecdn.teacherspayteachers.com/thumbuserhome/Patricia-Wallace-gomez-1702033781/266005.jpg)
Algebra 1 Complete Curriculum ( Common Core Aligned)
![more zero product law work common core algebra 1 homework](https://ecdn.teacherspayteachers.com/thumbuserhome/Infinitely-Pi-Learning-1699181694/2030813.jpg)
Common Core Algebra 1 VOCABULARY ACTIVITIES - BUNDLE PRICE!
![more zero product law work common core algebra 1 homework Preview of Business Math: Algebra 1 Common Core Project Based Learning](https://ecdn.teacherspayteachers.com/thumbitem/Business-Math-Algebra-1-Common-Core-Project-Based-Learning-4000679-1657535792/original-4000679-1.jpg)
Business Math: Algebra 1 Common Core Project Based Learning
![more zero product law work common core algebra 1 homework](https://ecdn.teacherspayteachers.com/thumbuserhome/Project-Math-1667237615/10217659.jpg)
Common Core Algebra 1 : STATISTICS UNIT - BUNDLE PRICE!
![more zero product law work common core algebra 1 homework Preview of Bundle: Algebra 1 Statistics Unit Curriculum (Common Core)](https://ecdn.teacherspayteachers.com/thumbitem/Bundle-Algebra-1-Statistics-Unit-Curriculum-Common-Core--4293392-1689478359/original-4293392-1.jpg)
Bundle: Algebra 1 Statistics Unit Curriculum ( Common Core )
![more zero product law work common core algebra 1 homework](https://ecdn.teacherspayteachers.com/thumbuserhome/Statistics-Education-Resources-1704623125/7384258.jpg)
Algebra 1 Common Core Data Analysis ENTIRE UNIT BUNDLE
![more zero product law work common core algebra 1 homework](https://ecdn.teacherspayteachers.com/thumbuserhome/Boom-Feeny-1721642571/3515180.jpg)
Pre Algebra 1 Algebraic Expressions Equations Review Common Core Math 6.EE.A.2
![more zero product law work common core algebra 1 homework Preview of Common Core Math 1/Algebra 1 Final Exam Review Bundle (5 products!)](https://ecdn.teacherspayteachers.com/thumbitem/Common-Core-Math-1-Algebra-1-Final-Exam-Review-Bundle-5-products--2318694-1513692499/original-2318694-1.jpg)
Common Core Math 1 / Algebra 1 Final Exam Review Bundle (5 products!)
![more zero product law work common core algebra 1 homework](https://ecdn.teacherspayteachers.com/thumbuserhome/Sarahs-School-Of-Math-1709980093/1622399.jpg)
Common Core Algebra 1 TASK CARDS - BUNDLE PRICE!
![more zero product law work common core algebra 1 homework Preview of Algebra 1 - Complete Curriculum Map (Common Core Aligned)](https://ecdn.teacherspayteachers.com/thumbitem/Algebra-1-Complete-Curriculum-Map-Common-Core-098456600-1378789869-1721007230/original-868307-1.jpg)
Algebra 1 - Complete Curriculum Map ( Common Core Aligned)
![more zero product law work common core algebra 1 homework Preview of Algebra 1 - Checklists for Common Core Standards](https://ecdn.teacherspayteachers.com/thumbitem/Algebra-1-Checklists-for-Common-Core-Standards-1412460-1470472523/original-1412460-1.jpg)
Algebra 1 - Checklists for Common Core Standards
![more zero product law work common core algebra 1 homework](https://ecdn.teacherspayteachers.com/thumbuserhome/Weatherly-1709809860/726160.jpg)
Piecewise-Defined Functions Algebra 1 Unit 6 | Bundle for Common Core
![more zero product law work common core algebra 1 homework Preview of Algebra 1 Unit Lesson Plan Word Templates Common Core Big Ideas Algebra 1](https://ecdn.teacherspayteachers.com/thumbitem/Algebra-1-Unit-Lesson-Plan-Word-Templates-Common-Core-Big-Ideas-Algebra-1-11942888-1722386264/original-11942888-1.jpg)
Algebra 1 Unit Lesson Plan Word Templates Common Core Big Ideas Algebra 1
![more zero product law work common core algebra 1 homework](https://ecdn.teacherspayteachers.com/thumbuserhome/The-Toolbox-For-Teachers-1723806792/357936.jpg)
Algebra 1 Common Core Mini Quizzes (End-of-Course Test Prep)
![more zero product law work common core algebra 1 homework Preview of Summer School Curriculum/Review for Algebra 1 Regents Common Core](https://ecdn.teacherspayteachers.com/thumbitem/Summer-School-Curriculum-Review-for-Algebra-1-Regents-Common-Core-4561445-1679626293/original-4561445-1.jpg)
Summer School Curriculum/Review for Algebra 1 Regents Common Core
![more zero product law work common core algebra 1 homework](https://ecdn.teacherspayteachers.com/thumbuserhome/Classy-Ashley-1672426092/12129481.jpg)
- We're hiring
- Help & FAQ
- Privacy policy
- Student privacy
- Terms of service
- Tell us what you think
Common Core Algebra II.Unit 6.Lesson 1.Quadratic Function Review
![more zero product law work common core algebra 1 homework more zero product law work common core algebra 1 homework](https://cdn.teachertube.com/sharedfiles/avatars/big/1941294.png)
emathinstruction
Oct 20, 2016
Learning Common Core Algebra II.Unit 6.Lesson 1. Quadratic Function Review by eMathInstruction
Embeddable Player
Related categories.
- $ 0.00 0 items
Unit 6 – Exponents, Exponents, Exponents and More Exponents
This unit begins with a fundamental treatment of exponent rules and the development of negative and zero exponents. We then develop the concepts of exponential growth and decay from a fraction perspective. Finally, percent work allows us to develop growth models based on constant percent rates of change. Geometric sequences are tied to exponential growth in the last lesson.
Simplifying Expressions Involving Exponents
LESSON/HOMEWORK
LECCIÓN/TAREA
LESSON VIDEO
EDITABLE LESSON
EDITABLE KEY
Zero and Negative Exponents
Exponential Growth and Decay
Introduction to Exponential Functions
Percent Review
Percent Increase and Decrease
Exponential Models Based on Percent Growth
Linear Versus Exponential
Geometric Sequences
Unit Review
Unit #6 Review – Exponents, Exponents, Exponents
UNIT REVIEW
REPASO DE LA UNIDAD
EDITABLE REVIEW
Unit #6 Assessment Form A
EDITABLE ASSESSMENT
Unit #6 Assessment Form B
Unit #6 Assessment Form C
Unit #6 Assessment Form D
Unit #6 Exit Tickets
Unit #6 Mid-Unit Quiz (Through Lesson #5) – Form A
Unit #6 Mid-Unit Quiz (Through Lesson #5) – Form B
Unit #6 Mid-Unit Quiz (Through Lesson #5) – Form C
U06.AO.01 – Negative and Zero Exponent Practice
EDITABLE RESOURCE
U06.AO.02 – Percent Warm-Up (Before Lesson #5)
U06.AO.03 – Interest Modeling Performance Task
U06.AO.04 – Additional Practice with Percent Increase and Decrease
Thank you for using eMATHinstruction materials. In order to continue to provide high quality mathematics resources to you and your students we respectfully request that you do not post this or any of our files on any website. Doing so is a violation of copyright. Using these materials implies you agree to our terms and conditions and single user license agreement .
The content you are trying to access requires a membership . If you already have a plan, please login. If you need to purchase a membership we offer yearly memberships for tutors and teachers and special bulk discounts for schools.
Sorry, the content you are trying to access requires verification that you are a mathematics teacher. Please click the link below to submit your verification request.
![](http://writinghelp.online/777/templates/cheerup/res/banner1.gif)
IMAGES
VIDEO
COMMENTS
Unit 8 - Quadratic Functions and Their Algebra These lessons introduce quadratic polynomials from a basic perspective. We then build on the notion of shifting basic parabolas into their vertex form. Completing the square is used as a fundamental tool in finding the turning point of a parabola. Finally, the zero product law is introduced as a way to find the zeroes of a quadratic function.
In this video, students review the Zero Product Law and then used it to find the zeroes of parabolas and cubic function, where appropriate factoring exists. Graphs of functions reinforce what is ...
The following lesson plans and worksheets are from the New York State Education Department Common Core-aligned educational resources. Eureka/EngageNY Math Algebra I Worksheets. These Lesson Plans and Worksheets are divided into five modules.
Find step-by-step solutions and answers to Algebra 1 Common Core - 9780133185485, as well as thousands of textbooks so you can move forward with confidence.
In this lesson, students learn how to solve a quadratic equation by factoring and using the zero product law.
COMMON CORE ALGEBRA II Date: _________________ We saw in Common Core Algebra I how any quadratic equation could be solved using the process of Completing the Square. This is reviewed in Exercise #1. Exercise #1: Solve the following quadratic equation for all values of x by first completing the square on the quadratic expression.
New York State Common Core Math Algebra I, Module 4, Lesson 5. Worksheets for Algebra 1. Lesson 5 Summary. Zero Product Property. If ab = 0, then a = 0 or b= 0 or a = b = 0. When solving for the variable in a quadratic equation, rewrite the equation as a factored quadratic set equal to zero. Using the zero product property, you know that if one ...
Lesson 5: The Zero Product Property Opening Exercise Consider the equation ∙ ∙ ∙ = 0. What values of , , , and
In this lesson we learn about the zero product law and how to use it, in conjunction with factoring, to find the zeroes or x-intercepts of a parabola. Watch Common Core Algebra I.Unit 8.Lesson 6.The Zeroes of a Quadratic, Algebra 1 Videos on TeacherTube.
Common Core Algebra 1. These interactive lessons use dynamic graphing and guided discovery to strengthen and connect symbolic and visual reasoning. They give the student a hands-on visual exposition of all Common Core Algebra 1 topics, reinforced by adaptive exercises and randomly generated tests. All exercises and tests are checked and graded ...
THE ZERO PRODUCT LAW. If the product of multiple factors is equal to zero then at least one of the factors must be equal to zero. The law can immediately be put to use in the first exercise. In this exercise, quadratic equations are given already in factored form. Exercise #1: Solve each of the following equations for all value(s) of x.
Lesson #2 - Unit Conversions #3 Nonproportional Linear Relationships #4 - More Work Graphing Linear Functions (Lines) #5 - Writing Equations in Slope-Intercept Form #6 - Modeling with Linear Functions #7 - More Linear Modeling #8 - Strange Lines - Vertical and Horizontal Lesson #9 - Absolute Value and Step Functions
Watch Common Core Algebra I.Unit 8.Lesson 7.More Zero Product Law, Math, Middle School, Math, Algebra Videos on TeacherTube.
Lesson 5: The Zero Product Property. ro Product PropertyExercises 1-4Find values of and that sati. y each of the following equations. (There m. ne cor. ct answer.)Exe. ci. es. 5 .
This concept introduces solving quadratic equations by factoring and using the zero product property.
Zero Product Property The "Zero Product Property" says that: If a × b = 0 then a = 0 or b = 0 (or both a=0 and b=0) It can help us solve equations:
Students solve increasingly complex one-variable equations, some of which need algebraic manipulation, including factoring as a first step and using the zero product property.
This Curriculum Bundle provides you with 12 full Units to teach the entire Algebra 1 Common Core Curriculum, consisting of a full school year's worth of 140 Lessons, Quizzes, Reviews & Tests. Each lesson includes a student worksheet, Smartnotebook file & PDF of the lesson and teacher answer keys. Many lessons have homework worksheets and a.
Unit 1 - The Building Blocks of Algebra This unit revolves around the concept of equivalency. Within this larger framework, we review and develop the real number properties and use them to justify equivalency amongst algebraic expressions. Students get work in mindful manipulation of algebraic expressions and actively seek structure within expressions to understand equivalency.
Lesson 6 The Zero Product Law LESSON/HOMEWORK LESSON VIDEO ANSWER KEY EDITABLE LESSON EDITABLE KEY
Watch Common Core Algebra II.Unit 6.Lesson 1.Quadratic Function Review, Math Videos on TeacherTube.
Unit 6 - Exponents, Exponents, Exponents and More Exponents. This unit begins with a fundamental treatment of exponent rules and the development of negative and zero exponents. We then develop the concepts of exponential growth and decay from a fraction perspective. Finally, percent work allows us to develop growth models based on constant ...