1. **State the problem:** Simplify or factor the quadratic expression $x^2 + 9x + 20$. 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, $a=1$, $b=9$, and $c=20$. We need two numbers that multiply to $1 \times 20 = 20$ and add to $9$. 4. The numbers $4$ and $5$ satisfy this because $4 \times 5 = 20$ and $4 + 5 = 9$. 5. Rewrite the middle term using these numbers: $$x^2 + 4x + 5x + 20$$ 6. Group terms: $$(x^2 + 4x) + (5x + 20)$$ 7. Factor each group: $$x(x + 4) + 5(x + 4)$$ 8. Factor out the common binomial: $$(x + 4)(x + 5)$$ **Final answer:** $$x^2 + 9x + 20 = (x + 4)(x + 5)$$