Solving Equations by Factoring

When the product of two numbers is 0, then one of the numbers must be 0.  This is a special property of 0 and does not apply to other numbers.  For example, if the product of two numbers is 8, then neither number need be 8 (2 times 4 is 8, so the numbers could be 2 and 4).

This property of 0 is called the "zero product property" and can be used to solve an equation when its factored form is equal to 0.

For example, the equation (x – 5)(x + 3) = 0 tells us that the product of the two numbers x – 5 and x + 3 is 0.  Therefore one of these numbers must be 0.  That is, either x – 5 = 0 or x + 3 = 0.  The solutions to these two equations are x = 5 and x = –3, so the equation (x – 5)(x + 3) = 0 has these two solutions.

Quadratic equations of the form ax² + bx + c = 0 can often be solved by factoring the left side, as the following examples illustrate.

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