Solve the quadratic equation: x^2 - 5x - 6 = 0

• A. x = 6 or x = -1
• B. x = -6 or x = 1
• C. x = 3 or x = -2
• D. x = 5 or x = -1

Answer: (A)

To solve by factoring, look for two numbers that multiply to the constant term (-6) and add to the coefficient of x (-5). Those numbers are -6 and 1, since (-6) × 1 = -6 and (-6) + 1 = -5. So the quadratic factors as (x − 6)(x + 1) = 0. By the zero-product property, either x − 6 = 0 or x + 1 = 0, giving x = 6 or x = -1. You can verify quickly by substitution: 6^2 − 5·6 − 6 = 0 and (−1)^2 − 5(−1) − 6 = 0. The solutions are 6 and -1.