The Zero Product Property - Varsity Tutors

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The Zero Product Property

Study Guide

Key Definition

The Zero Product Property states that if $ab = 0$, then either $a = 0$ or $b = 0$ (or both).

Important Notes

  • A product is zero if at least one factor is zero.
  • Used primarily in solving quadratic equations.
  • Helps to simplify equations by factoring.
  • Essential for understanding polynomial solutions.
  • Allows breaking down complex equations into simpler parts.

Mathematical Notation

$ab = 0$ means either $a = 0$ or $b = 0$$x^2$ represents x squared$=$ represents equalityRemember to use proper notation when solving problems

Why It Works

The Zero Product Property allows us to find the roots of a polynomial equation by setting each factor equal to zero and solving for the variable.

Remember

When faced with an equation like $(x+5)(x-4) = 0$, set each factor equal to zero: $x+5 = 0$ and $x-4 = 0$.

Quick Reference

Property:$ab = 0 \implies a = 0 \text{ or } b = 0$

Understanding The Zero Product Property

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Video explanation of this concept

concept. Use space or enter to play video.concept thumbnailBeginner

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Beginner Explanation

Simple explanation with $ab = 0 \implies a = 0 \text{ or } b = 0$Now showing Beginner level explanation.

Practice Problems

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1

Quick Quiz

Single Choice QuizBeginner

What is the solution to $(x + 3)(x - 2) = 0$?

A$x = -3 \text{ or } x = 2$B$x = 3 \text{ or } x = -2$C$x = 0 \text{ or } x = 5$D$x = 1 \text{ or } x = -1$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

You are designing a rectangular garden. The area is given by $x(x - 7) = 0$. What are the possible lengths of one side?Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Consider the equation $y(y + 6) = 0$. Find the values of $y$ that satisfy the equation.

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

Solve $(2x + 1)(x - 3) = 0$

A$x = -\frac{1}{2} \text{ or } x = 3$B$x = \frac{1}{2} \text{ or } x = -3$C$x = 2 \text{ or } x = -1$D$x = 0 \text{ or } x = 3$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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