The Zero Product Property

The Zero Product Property simply states that if ab = 0, then either a = 0 or b = 0 (or both). A product of factors is zero if and only if one or more of the factors is zero.

This is particularly useful when solving quadratic equations.

Example:

Suppose you want to solve the equation

x2 + x – 20 = 0.

You can factor the left side as:

(x + 5)(x – 4) = 0

Now, by the zero product property, either

x + 5 = 0   or   x – 4 = 0,

which means either x = –5 or x = 4. These are the two solutions of the equation.