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. This property is fundamental in solving quadratic equations by factoring.

5 Must Know Facts For Your Next Test

1. If $ab = 0$, then either $a = 0$ or $b = 0$ (or both).
2. To solve a quadratic equation using the zero-product property, first rewrite the equation in standard form $ax^2 + bx + c = 0$.
3. Factoring the quadratic expression into a product of binomials allows the use of the zero-product property.
4. Once factored, set each factor equal to zero and solve for $x$ to find the roots of the equation.
5. The zero-product property is only applicable when the product equals zero; it does not apply to other constants.

Review Questions

• How do you apply the zero-product property to solve a factored quadratic equation?
• What steps are involved in rewriting a quadratic equation before applying the zero-product property?
• Why does the zero-product property not apply if the product of two factors is not equal to zero?

Related terms

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

Factoring: The process of breaking down an expression into a product of simpler expressions or factors.

Roots: The solutions to an equation; for a quadratic equation, these are the values of $x$ that satisfy $ax^2 + bx + c = 0$.