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.