Zero Product Property

Date: 02/14/98 at 12:42:56
From: Jessica
Subject: Zero Product Property

How do you find the answer to a zero product property question? If you 
could help it would be very helpful!

Date: 02/17/98 at 21:48:48
From: Doctor Schwenoha
Subject: Re: Zero Product Property

The zero product property simply states that if the result of 
multiplying two or more numbers is zero, then one (or more) of the 
numbers must be zero. 

So, if AB = 0 then A = 0, B = 0, or both A and B are equal to zero.  

You could extend this to ABC = 0 and surmise that one of the three 
equals zero, or it could be that two of them equal zero or that all 
three equal zero. Take this thought to as many factors as you wish.

Let's look at some typical algebra problems dealing with this 
property.

    x^2 - x = 0    factors to
     x(x-1) = 0    so we have two factors and either of them could 
                   equal zero.  

Set up both of them equal to zero to solve for the possibilities: 

          x = 0     or     x - 1 = 0
                               x = 1

We now have the solution that x = 0 or 1 to make our original equation 
true. 

Another problem might be     x^2 - x - 6 = 0  this factors to
                          (x + 2)(x - 3) = 0  and one of those factors 
                                              must be zero, so either

      x + 2 = 0      or    x - 3 = 0      and the solutions are                      
          x = -2     or        x = 3

Now that you know the process for using the zero product property, 
what does it do for you? What do these possible values for x do for 
you?  If you were graphing either of the equations in these examples, 
the solutions for x would tell you where the graph of the equation 
crosses the x-axis. In your algebra course of study I would guess that 
you are building to a place where you will need to use this 
information.       

-Doctor Schwenoha,  The Math Forum
 Check out our Web site http://mathforum.org/dr.math/