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The zero product property worksheets

If two numbers multiply to zero, one of them is zero. That one sentence solves (x − 14)(x − 6) = 0 without expanding anything, and these free printable worksheets give eight equations that are already factored, so it is the only thing being practised.

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The zero product property
The zero product property worksheet — Already factored, roots to ±20, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

With the factoring taken away, what is left is the step students get wrong while believing they have it. (x + 2)(x − 20) = 0 does not give x = 2 and x = −20; it gives x = −2 or x = 20, because x + 2 is zero when x is −2. The number in a bracket is the root with its sign turned over, every time, and a page of nothing else makes that a reflex rather than a rule to recall.

Why this sheet works

The answer key writes the property out the way it is used: x + 2 = 0 or x − 20 = 0, each one solved on its own line, then the pair. That “or” line is the habit worth building. It is what stops a student from reading the roots straight off the brackets, and it is the same line they will need once the brackets have to be found first.

How this one works

(x + 3)(x + 8) = 0

(x + 3)(x + 8) = 0
(x + 3)(x + 8) = 0
x + 3 = 0orx + 8 = 0
x + 3 = 0→x = −3
x + 8 = 0→x = −8
x = −3orx = −8
  1. The left side is already a product of two brackets, and the right side is zero. So no factoring is needed.
  2. If two things multiply to zero, one of them must be zero. So either (x + 3) is zero, or (x + 8) is zero.
  3. Solve each one. x + 3 = 0 gives x = −3, and x + 8 = 0 gives x = −8. Notice the sign turns over: a + in the bracket gives a negative answer.
  4. So x = −3 or x = −8. Either one makes the equation true.

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