## Related Words

# 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.

### More About Zero-Product Property

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

**Ques: **Consider this simple algebra problem. Solve x^{2} -4x = 0.

#### Solution:

Let's solve this equation through factoring, followed by the application of the Zero-Product Property

x^{2}-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 x^{2} - 4x = 0

### Video Examples: The Zero-Product Property

### Solved Example on Zero-Product Property

**Ques: **Solve for x: x^{2} + 4x - 5 = 0

#### Solution:

- x
^{2}+ 4x - 5 = 0

⇒ x^{2}+ 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 x
^{2}+ 4x - 5 = 0.