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 x2 -4x = 0.
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
Video Examples: The Zero-Product Property
Solved Example on Zero-Product Property
Ques: Solve for x: x2 + 4x - 5 = 0
- 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.