Final answer:
To solve the quadratic equation x² - 2x - 15 = 0 by factoring, find two numbers that multiply to -15 and add up to -2. The solutions to the equation are x = 5 and x = -3.
Step-by-step explanation:
To solve the quadratic equation x² - 2x - 15 = 0 by factoring, we need to find two numbers that multiply to -15 and add up to -2 (the coefficient of x). In this case, the numbers are -5 and 3. Therefore, we can write the equation as (x - 5)(x + 3) = 0. Setting each factor equal to zero, we find x - 5 = 0, giving x = 5, and x + 3 = 0, giving x = -3. So the solutions to the quadratic equation are x = 5 and x = -3.