EMS Homework Help

## 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.
In simpler words:
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.

• A. – 1, 5
• B. 1, 5
• C. – 5, - 1
• D. 1, - 5
First
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]
1.              (     5)(  - 1)
2.              (      5)(x  - 1)
3.              (x + 5)( x  -  1)
4.              (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