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
Common Core Algebra II - Unit #6 Quadratic Functions and Their Algebra
Description
Quadratic functions and their ties to polynomial algebra are thoroughly explored in this 11 lesson unit. All major types of factoring techniques are developed, including factoring by grouping. The Zero Product Law is reviewed and used to solve quadratic equations and inequalities, including those arising from modeling contexts. Finally equations of circles and parabolas are developed from their formal locus definitions.
To access the lesson videos on YouTube use your smartphone or tablet to scan the QR code at the top of each lesson.
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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.
In this video, we use the Zero Product Law to solve quadratic equations. The first set is already factored, while the second set we factor.Please leave ques...
Common Core Algebra II; Algebra 2 + Trigonometry; Standards Alignment; Shop. N-Gen Math™ 6; N-Gen Math™ 7; ... LESSON/HOMEWORK. LESSON VIDEO. ANSWER KEY. EDITABLE LESSON. EDITABLE KEY. Lesson 2 Factoring. ... The Zero Product Law. LESSON/HOMEWORK. LESSON VIDEO. ANSWER KEY. EDITABLE LESSON. EDITABLE KEY.
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For the 15 years that a computer store has been open, its annual revenue R (in millions of dollars) can be modeled by $$ R=-0.0040t^4+0.088t^3-0.36t^2-0.55t+5.8 $$ where t is the number of years since the store opened.
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. ... The zero product property states that if a⋅b=0 then either a or b equal zero. This basic property ...
Since the product equals 0, then at least one of the factors on the left-hand side must equal zero. So we can find the two solutions by setting each factor equal to zero and solving each equation separately. Setting the factors equal to zero gives us: (x + 6) = 0 OR (2x − 7) = 0. Solving both of those equations gives us: x + 6 = 0 2x − 7 ...
Watch Common Core Algebra II.Unit 6.Lesson 6.The Zero Product Law, Math, Middle School, Math, Algebra Videos on TeacherTube. X. Find Lessons! Join Free! ... Common Core Algebra II.Unit 6.Lesson 6.The Zero Product Law Middle School / Math / Algebra. emathinstruction. Oct 20, 2016. 8112 views.
Algebra Polynomials and Factoring ..... All Modalities. More All Modalities; Share with Classes. ... This concept introduces solving quadratic equations by factoring and using the zero product property. ... Common Core Math; College FlexBooks; K-12 FlexBooks; Tools and Apps; v2.10.18.20240308074534-ff36bc110 ...
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 5 M4 ALGEBRA I Lesson 5: The Zero Product Property Exercises 1-4 Find values of and that satisfy each of the following equations. (There may be more than one correct answer.) 1. 2. 3. 4.
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. ...
Exercise #1: Solve the following quadratic equation for all values of x by first completing the square on the quadratic expression. Express your answers in simplest radical form. x. 2 6 x 1 0. Since any quadratic can be rearranged through the process of Completing the Square, a formula can be developed that will solve for the roots of any ...
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
Description. Quadratic functions and their ties to polynomial algebra are thoroughly explored in this 11 lesson unit. All major types of factoring techniques are developed, including factoring by grouping. The Zero Product Law is reviewed and used to solve quadratic equations and inequalities, including those arising from modeling contexts.
Plus or minus the square root of negative ten squared minus four times a times C, all divided by two times a again, being careful. Negative ten squared is positive 100. Minus four times one times 20, which would be 80. That's going to be ten plus or minus square root of 20. All over two, now we have to be careful.
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 ...
Exercise 8. Exercise 9. Exercise 10. Exercise 11. Exercise 12. Exercise 13. Exercise 14. Exercise 15. Find step-by-step solutions and answers to Algebra 2 Common Core - 9780133186024, as well as thousands of textbooks so you can move forward with confidence.
The Zero Product Law can be used to solve any quadratic equation that is factorable (not prime). To utilize this technique the problem solver must first set the equation equal to zero and then factor the non-zero side. Exercise #3: Solve each of the following quadratic equations using the Zero Product Law.
Our resource for Algebra 2: Homework Practice Workbook includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. With Expert Solutions for thousands of practice problems, you can take the guesswork out of studying and move forward with confidence. Find step-by-step solutions and answers ...
In this lesson, students learn how to solve a quadratic equation by factoring and using the zero product law.
The zero product law is a fundamental concept in algebra that states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.This concept is used frequently in solving equations and factoring polynomials. the question of the zero product law common core algebra 2 homework answers is that the zero product law is a concept used in ...
• Lesson #5 - The Method of Common Bases • Lesson #6 - Exponential Modeling with Percent Growth and Decay • Lesson #7 - Mindful Percent Manipulations ... • Lesson #6 - The Zero Product Law • Lesson #7 - Quadratic Inequalities in One Variable • Lesson #8 - Completing the Square and Shifting Parabolas ...
You worked with this extensively in Common Core Algebra I. The first exercise will review how to use a method known as completing the square. to identify shifts and the turning point of a parabola. Exercise #1: The function y x 2 is shown already graphed on the grid below. Consider the quadratic whose equation is y x.