Solve by factoring.s squared plus 8 s plus 15 equals 0Question content area bottomPart 1The solution is s ​=enter your response here.​(Use a comma to separate answers as​ needed.)

Answer 1

To solve the quadratic equation \( s^2 + 8s + 15 = 0 \) by factoring, we need to factor the quadratic expression on the left.

1. We look for two numbers that multiply to \( 15 \) (the constant term) and add to \( 8 \) (the coefficient of \( s \)).
2. The numbers \( 3 \) and \( 5 \) fit, since \( 3 \times 5 = 15 \) and \( 3 + 5 = 8 \).

Thus, we can factor the quadratic expression as:

\[ (s + 3)(s + 5) = 0 \]

3. Now, we set each factor equal to zero:

\[ s + 3 = 0 \quad \text{or} \quad s + 5 = 0 \]

4. Solving these gives us:

\[ s = -3 \quad \text{or} \quad s = -5 \]

Therefore, the solution to the equation \( s^2 + 8s + 15 = 0 \) is:

\[ s = -3, -5 \]

So you can enter your response as:

\(-3, -5\)