﻿ Definition of Zero-Product Property | Define Zero-Product Property - Free Math Dictionary Online

# ZERO-PRODUCT PROPERTY

## Definition of Zero-Product Property

If the product of two or more factors is zero then at least one of the factors should be zero. This property is known as Zero-Product Property.

That is, if XY = 0, then X = 0 or Y = 0 or both X and Y are equal to 0.
Similarly, if XYZ = 0, then X = 0 or Y = 0 or Z = 0 or all three are 0.
This thought can be extended to any number of factors.

The x-coordinate of the point where a line intersects the y-axis is 0. So, the y-intercept of a line can also be found by substituting x = 0 in the equation of the line.

### Examples of Zero-Product Property

#### Solution:

Let's solve this equation through factoring, followed by the application of the Zero-Product Property
x2-4x = 0 ⇒ x (4 - x) = 0 [Taking out the common variable x]
⇒ x = 0 or (4 - x) = 0 [Recall the definition of Zero-product Property.]
⇒ x = 0 or x = 4
So, the solutions are x = 0 or x = 4
Both these values satisfy the original equation x2 - 4x = 0

### Solved Example on Zero-Product Property

#### Solution:

• x2 + 4x - 5 = 0
⇒ x2 + 5x - x - 5 = 0 [Splitting the middle term]
• ⇒ x(x + 5) - 1(x+5) = 0 [Taking out the common factors]
• (x + 5)(x - 1) = 0 [Factor.]
• ⇒ x + 5 = 0 or (x - 1) = 0 [Recall the definition of Zero-product property.]
• ⇒ x = -5 or x = 1
• So, the solutions are x = -5 or x = 1
• Both these values satisfy the original equation x2 + 4x - 5 = 0.

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