1. **State the problem:** Factor the quadratic expression $m^2 + 18m + 17$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multiply to $ac$ and add to $b$. 3. Here, $a=1$, $b=18$, and $c=17$. We need two numbers that multiply to $1 \times 17 = 17$ and add to $18$. 4. The numbers are $1$ and $17$ because $1 \times 17 = 17$ and $1 + 17 = 18$. 5. Rewrite the middle term using these numbers: $$m^2 + 1m + 17m + 17$$ 6. Group terms: $$(m^2 + 1m) + (17m + 17)$$ 7. Factor each group: $$m(m + 1) + 17(m + 1)$$ 8. Factor out the common binomial: $$(m + 1)(m + 17)$$ **Final answer:** The factored form of $m^2 + 18m + 17$ is $$\boxed{(m + 1)(m + 17)}$$