Solve an equation using the zero product property

Learning Objectives Define the Zero Product Property in their own words. Identify when an equation is in the correct form to apply the Zero Product Property. Solve quadratic equations that are already in factored form. Rearrange a quadratic equation into standard form (ax² + bx + c = 0) before solving. Factor a quadratic expression and then use the Zero Product Property to find the solutions. Verify the solutions to a quadratic equation by substituting them back into the original equation. If you multiply two secret numbers together and the answer is zero, what can you say for sure about at least one of those numbers? 🤔 This lesson introduces a powerful shortcut for solving certain equations called the Zero Product Property. You will learn how to use your factoring skills...

TermDefinitionExample Zero Product PropertyA rule stating that if the product of two or more factors is zero, then at least one of the factors must be equal to zero.If (x + 2)(x - 3) = 0, then either x + 2 = 0 or x - 3 = 0. FactorAn algebraic expression that is multiplied with other expressions to form a product.In the expression (x + 5)(x - 1), the factors are (x + 5) and (x - 1). Factored FormA quadratic expression written as a product of its linear factors.The factored form of x² + 3x - 10 is (x + 5)(x - 2). RootA value of the variable that makes an equation true. For a quadratic equation, the roots are the x-values where its graph intersects the x-axis.For the equation x² - 9 = 0, the roots are x = 3 and x = -3. Quadratic EquationAn equation that can be written in the standard form ax...

The Zero Product Property If A \cdot B = 0, then A = 0 \text{ or } B = 0. Use this rule after you have an equation where one side is a product of factors and the other side is zero. Set each factor equal to zero individually and solve. Standard Form of a Quadratic Equation ax^2 + bx + c = 0 Before you can factor and solve, you must rearrange the equation so that all terms are on one side, set equal to zero. This is the required starting format.