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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.
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.