## The Zero-Product Property

Overview: In this lesson you will learn about the zero-product property and how to solve an equation using it.

**Zero - Product Property**

**Definition of Zero - Product Property**

- Zero - Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.

ab = 0

(or another set of variables=0)

than either

a=0 and/or b=0

because there's no other way the product could give zero.

So if we can write a quadratic equation as a couple of factors giving zero, then we can set each of those factors equal to zero and solve them independently to find the solutions to the original equation!

**Examples of Zero - Product Property**

- If
*xy*= 0, then*x*= 0 and/or*y*= 0.

**Answer Choices:**

- A. – 1, 5

- B. 1, 5
- C. – 5, - 1
- D. 1, - 5

Outer

Inner

Last

## Step one

[Write out the entire problem]

**Step 2:**(

*x*+ 5)(

*x*– 1) = 0 [Turn into 2 separate equations by using FOIL backwards: 5-1, 5x, x1, xx]

- ( 5)( - 1)
- ( 5)(x - 1)
- (x + 5)( x - 1)
- (x + 5)(x - 1)

**Step 3:**

*x*+ 5 = 0 or

*x*– 1 = 0 [Applying Zero-product property.]

**Step 4:**

*x*+ 5 – 5 = 0 – 5 or

*x*– 1 + 1 = 0 + 1 [Simplify the equations.]

**S**

**tep 5:**

*x*= - 5 or

*x*= 1

**Step 6:**The solutions for the equation (

*x*+ 5)(

*x*– 1) = 0 are 1 and – 5.

The correct answer is: D 1,-5

All problems/information comes directly from: http://www.northstarmath.com/sitemap/zero-productproperty.html

Also information from: http://answers.yahoo.com/question/index?qid=20100425213028AAysXLl, from Answerer 1

I do not own any of this information. Thanks reliable resources, I want to give you credit for being so smart!

Also information from: http://answers.yahoo.com/question/index?qid=20100425213028AAysXLl, from Answerer 1

I do not own any of this information. Thanks reliable resources, I want to give you credit for being so smart!