Final answer:
To factor the quadratic equation x^2 + 8x + 15 = 0, we find that the factored form is (x + 3)(x + 5) = 0, which gives the solutions x = -3 and x = -5.
Step-by-step explanation:
To factor the quadratic equation x^2 + 8x + 15 = 0, we are looking for two numbers that multiply to give the constant term (15) and add up to give the coefficient of the linear term (8). These two numbers are 3 and 5 because 3 × 5 = 15 and 3 + 5 = 8. Therefore, the factored form of the equation is (x + 3)(x + 5) = 0.
When an equation is factored, we can use the zero product property to find the values of x that satisfy the equation. This means setting each factor equal to zero and solving for x:
- x + 3 = 0 → x = -3
- x + 5 = 0 → x = -5
So, the solutions to the equation are x = -3 and x = -5.