Solve x^2 - 4x - 5 = 0 by factoring. Which of the following lists the solutions?

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

Answer: (A)

When a quadratic is set to zero, factoring helps by turning it into a product of binomials. You want two numbers that multiply to the constant term (-5) and add to the coefficient of x (-4). Those numbers are -5 and 1, since (-5)·1 = -5 and (-5) + 1 = -4. So the quadratic factors as (x − 5)(x + 1) = 0.

Setting each factor to zero gives x − 5 = 0 or x + 1 = 0, so x = 5 or x = −1. These satisfy the equation (check: 5^2 − 4·5 − 5 = 0 and (−1)^2 − 4(−1) − 5 = 0).