What does the zero factor property mean?

We start by defining the Zero-Product Property

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

That is, if XY = 0, then X = 0 or Y = 0 or both X and Y are 0.

Similarly, if XYZ = 0, then X = 0 or Y = 0 or Z = 0 or all three are 0.

Examples of Zero-Product Property

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.

On factoring,

x2 – 4x = 0 Þ x (4 – x) = 0

x (4 – x) = 0 Þ x = 0 or (4 – x) = 0 [Recall the definition of Zero-product Property.]

Þ x = 0 or x = 4

So, the solutions are x = 0 or x = 4. Both these values satisfy the original equation x2 – 4x = 0.