Zero Product
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:
  1. x = 0, and y ≠ 0
  2. y = 0, and x ≠ 0
  3. 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.
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