1. **State the problem:** Factor the quadratic expression $s^2 + 6s + 5$ into the product of two binomials. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, the factored form is $(x + m)(x + n)$ where $m$ and $n$ satisfy: $$m + n = b$$ $$mn = c$$ 3. **Apply to the problem:** Here, $a=1$, $b=6$, and $c=5$. We need two numbers $m$ and $n$ such that: $$m + n = 6$$ $$mn = 5$$ 4. **Find the numbers:** The pairs of factors of 5 are (1, 5) and (-1, -5). Check sums: - $1 + 5 = 6$ (matches $b$) - $-1 + (-5) = -6$ (does not match) 5. **Write the factored form:** Using $m=1$ and $n=5$, the factorization is: $$ (s + 1)(s + 5) $$ 6. **Verify by expansion:** $$ (s + 1)(s + 5) = s^2 + 5s + 1s + 5 = s^2 + 6s + 5 $$ **Final answer:** $$\boxed{(s + 1)(s + 5)}$$