The Zero-Product Property and Equations

Algebra Foundation

Algebra 1

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Algebra 1 · Unit 8 · Topic 8.5

The Zero-Product Property and Equations

For real factors, a product equals zero only if at least one factor equals zero.

Definition and explanation

For real factors, a product equals zero only if at least one factor equals zero. Move all terms of a polynomial equation to one side before applying this property to a factored expression.

Worked example

Solve x² − 5x = 14. Rearrange to x² − 5x − 14 = 0 and factor (x − 7)(x + 2) = 0. Thus x = 7 or x = −2; each gives 14 in x² − 5x.

Common mistake

Setting each factor equal to zero is valid for a product equal to zero, not a product equal to 14.

Key takeaway

For real factors, a product equals zero only if at least one factor equals zero.

Explain each step of the worked example, then check the units, signs, and conditions that apply.

Further reading

Topic coverage was checked against the openly available OpenStax Elementary Algebra 2e and Algebra and Trigonometry 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.