Solve the quadratic equation: x^2 - 4x - 5 = 0

• A. x = 5 or x = -1
• B. x = -5 or x = 1
• C. x = 4 or x = -5
• D. x = 0 or x = 1

Answer: (A)

Factoring a quadratic is a quick way to solve when it neatly breaks into linear factors. For x^2 - 4x - 5, look for two numbers that multiply to the product ac = -5 and add to the middle coefficient b = -4. Those numbers are -5 and 1. Rewrite the middle term using them: x^2 - 5x + x - 5. Group terms to factor: x(x - 5) + 1(x - 5) = (x - 5)(x + 1). Set each factor equal to zero: x - 5 = 0 or x + 1 = 0, giving x = 5 or x = -1. These are the solutions.