To factor the quadratic expression \( s^2 + 4s + 3 \), we need to find two numbers that multiply to the constant term (3) and add up to the coefficient of the linear term (4).
The numbers that satisfy these conditions are 1 and 3, since:
- \( 1 \times 3 = 3 \) (they multiply to 3)
- \( 1 + 3 = 4 \) (they add up to 4)
Thus, we can factor the expression as follows:
\[ s^2 + 4s + 3 = (s + 1)(s + 3) \]
So, the factored form of \( s^2 + 4s + 3 \) is \( (s + 1)(s + 3) \).