Solve a quadratic equation by factoring

Learning Objectives Identify and write a quadratic equation in standard form. Explain and apply the Zero Product Property to solve equations. Factor quadratic trinomials where the leading coefficient is 1. Factor quadratic trinomials where the leading coefficient is greater than 1. Solve quadratic equations involving special cases, such as a difference of squares or a greatest common factor. Verify the solutions (roots) of a quadratic equation by substituting them back into the original equation. If you throw a basketball, how can you predict the exact moment it hits the ground? 🏀 The answer lies in solving a quadratic equation! This tutorial will teach you a powerful algebraic method to solve quadratic equations: factoring. You will learn how to break down complex equatio...

TermDefinitionExample Quadratic EquationAn equation that can be written in the standard form ax² + bx + c = 0, where a, b, and c are constants and 'a' is not equal to zero. Its graph is a parabola.x² - 3x + 2 = 0 is a quadratic equation where a=1, b=-3, and c=2. Standard FormThe form ax² + bx + c = 0. It is essential to arrange the equation in this form before you begin factoring.The equation 5x = 6 - 2x² is written in standard form as 2x² + 5x - 6 = 0. FactoringThe process of breaking down a polynomial into a product of simpler polynomials (its factors).The quadratic expression x² + 5x + 6 can be factored into (x + 2)(x + 3). Zero Product PropertyA fundamental rule stating that if the product of two or more factors is zero, then at least one of the factors must be zero.If (x +...

Standard Form of a Quadratic Equation ax^2 + bx + c = 0 Before solving, you must arrange the equation so that all terms are on one side, set equal to zero. The term with x² should ideally have a positive coefficient 'a'. The Zero Product Property If A \cdot B = 0, then A = 0 \text{ or } B = 0 This is the core principle for solving by factoring. Once the quadratic is factored into a product of binomials, set each binomial factor equal to zero and solve for the variable. Difference of Squares a^2 - b^2 = (a - b)(a + b) A common factoring pattern to recognize when a quadratic has two terms that are perfect squares separated by a subtraction sign.