Zero Product
When the product of any number of terms is zero, you know
that at least one of the terms is equal to zero. For example, if xy =
0, you know that either:
-
x = 0, and y ≠ 0
- y =
0, and x ≠ 0
- x
= y = 0.
This is useful in a situation like the following:
In this equation, either x = –4 or x =
3, since one of the expressions in parentheses must be equal to
0.
Consider this equation:
Again, since 3x2 or
(x + 2) must equal 0, we know that either x =
0 or x = –2.
Keep your eye out for a zero product—it’s a big time-saver,
especially when you have multiple-choice answers to choose from.
(x-3).gif)
=0.gif)
