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Algebra 101 - Unit 5

Lesson 32: Solving Quadratic Equations by Factoring

Quadratic equations are equations of the form ax² + bx + c = 0. One of the most common methods for solving them is factoring.

Steps to Solve by Factoring

  1. Write the quadratic equation in standard form (ax² + bx + c = 0).
  2. Factor the quadratic completely.
  3. Set each factor equal to zero (Zero Product Property).
  4. Solve each simple equation to find the solutions.

Examples

Example 1: Solve x² + 5x + 6 = 0

  1. Factor: (x + 2)(x + 3) = 0
  2. Set each factor to zero: x + 2 = 0 or x + 3 = 0
  3. Solve: x = −2 or x = −3

Example 2: Solve 2x² + 7x + 3 = 0

  1. Factor: (2x + 1)(x + 3) = 0
  2. Set factors to zero: 2x + 1 = 0 or x + 3 = 0
  3. Solve: x = −1/2 or x = −3

Practice Problems

  1. Solve x² − 9x + 20 = 0
  2. Solve x² + 7x + 10 = 0
  3. Solve 3x² + 11x + 6 = 0
  4. Solve 4x² − 12x + 9 = 0