Solving Quadratic Equations by Factoring
Aligned to A-REI.B.4 — Common Core State Standards for Mathematics.
What this lesson teaches
A quadratic equals zero when either factor equals zero (the Zero Product Property). Factor, set each factor to 0, and solve.
Worked examples
Example 1
x² + 5x + 6 = 0 → (x+2)(x+3) = 0 → x = −2 or x = −3.
Example 2
x² − 7x + 12 = 0 → (x−3)(x−4) = 0 → x = 3 or x = 4.
Example 3
Factoring only works against zero. From x² + 5x + 6 = 2 you must first write x² + 5x + 4 = 0.
Practice questions
- Solve x² − 7x + 12 = 0.
- Solve x² − 9 = 0.
- Why does the Zero Product Property work?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Resolución de Ecuaciones Cuadráticas por Factorización
Una ecuación cuadrática es igual a cero cuando cualquiera de sus factores es igual a cero (Propiedad del Producto Nulo). Factoriza, iguala cada factor a 0 y resuelve.
Ejemplo 1: x² + 5x + 6 = 0 → (x+2)(x+3) = 0 → x = −2 o x = −3.
Ejemplo 2: x² − 7x + 12 = 0 → (x−3)(x−4) = 0 → x = 3 o x = 4.
Ejemplo 3: Factorizar solo funciona contra cero. De x² + 5x + 6 = 2 primero debes escribir x² + 5x + 4 = 0.
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