Zero-product property

Definition

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero. It is commonly used to solve quadratic equations by factoring.

5 Must Know Facts For Your Next Test

1. The zero-product property can only be applied when the equation is set to zero.
2. To use the property, factor the quadratic equation completely.
3. Once factored, set each factor equal to zero and solve for the variable.
4. The solutions obtained from setting each factor to zero are called roots or zeros of the equation.
5. This property is essential for solving polynomial equations and finding intercepts on graphs.

Review Questions

• How do you apply the zero-product property to a factored quadratic equation?
• Why must an equation be set to zero before using the zero-product property?
• What are the steps involved in solving a quadratic equation using the zero-product property?

Related terms

Quadratic Equation: An equation of the form $ax^2 + bx + c = 0$ where $a$, $b$, and $c$ are constants and $a \neq 0$.

Factorization: The process of breaking down an expression into a product of simpler expressions that can be multiplied together to get back the original expression.

Roots: The solutions of an equation where it equals zero. For quadratics, these are also known as zeros or x-intercepts.