1. **State the problem:** Factor the trinomial $$x^2 + 5x + 6$$. 2. **Recall the factoring formula:** For a trinomial of the form $$x^2 + bx + c$$, we look for two numbers that multiply to $$c$$ and add to $$b$$. 3. **Identify values:** Here, $$b = 5$$ and $$c = 6$$. 4. **Find two numbers:** We need two numbers that multiply to 6 and add to 5. These numbers are 2 and 3 because $$2 \times 3 = 6$$ and $$2 + 3 = 5$$. 5. **Write the factors:** The trinomial factors as $$(x + 2)(x + 3)$$. 6. **Check by FOIL:** $$\begin{aligned} (x + 2)(x + 3) &= x \times x + x \times 3 + 2 \times x + 2 \times 3 \\ &= x^2 + 3x + 2x + 6 \\ &= x^2 + 5x + 6 \end{aligned}$$ 7. **Final answer:** $$(x + 2)(x + 3)$$