Solve a quadratic equation by factoring

Learning Objectives Identify a quadratic equation and write it in standard form (ax^2 + bx + c = 0). Apply the Zero Product Property to find solutions from a factored quadratic equation. Factor quadratic trinomials where the leading coefficient 'a' is 1. Factor quadratic trinomials where the leading coefficient 'a' is not 1, using methods like grouping. Recognize and factor special cases, including the difference of squares and perfect square trinomials. Solve a complete quadratic equation by first factoring it and then applying the Zero Product Property. Interpret the solutions (roots) of a quadratic equation as the x-intercepts of the corresponding parabolic function. Ever wondered how to calculate the exact path of a basketball for a perfect shot? 🏀...

TermDefinitionExample Quadratic EquationA second-degree polynomial equation in a single variable x, which can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants and 'a' is not equal to zero.2x^2 - 5x + 3 = 0 is a quadratic equation where a=2, b=-5, and c=3. Standard FormThe conventional form of a quadratic equation, ax^2 + bx + c = 0, where all terms are on one side of the equation, set equal to zero, and arranged in descending order of their exponents.The equation 3x = 5 - 2x^2 in standard form is 2x^2 + 3x - 5 = 0. FactoringThe process of decomposing a polynomial into a product of simpler polynomials (its factors). When these factors are multiplied together, they result in the original polynomial.The polynomial x^2 + 5x + 6 can be factored into (x + 2)(x...

Standard Form of a Quadratic Equation ax^2 + bx + c = 0 Before attempting to factor, always rearrange the equation into this form. This ensures all terms are accounted for and sets the equation equal to zero, which is necessary for applying the Zero Product Property. 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 (or other factors), set each individual factor equal to zero and solve the resulting linear equations. Difference of Squares a^2 - b^2 = (a - b)(a + b) Use this special pattern to quickly factor binomials that consist of two perfect squares separated by a subtraction sign. This is a common shortcut.