The Zero Product Property

The Zero Product Property simply states that if a b = 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

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.

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