1. **State the problem:** Factor the quadratic expression $$w^2 + 8w + 15$$. 2. **Recall the factoring formula:** For a quadratic expression $$ax^2 + bx + c$$, we look for two numbers that multiply to $$ac$$ and add to $$b$$. 3. **Apply to our problem:** Here, $$a=1$$, $$b=8$$, and $$c=15$$. We need two numbers that multiply to $$1 \times 15 = 15$$ and add to $$8$$. 4. **Find the numbers:** The numbers $$3$$ and $$5$$ satisfy this because $$3 \times 5 = 15$$ and $$3 + 5 = 8$$. 5. **Write the factored form:** Using these numbers, the expression factors as: $$w^2 + 8w + 15 = (w + 3)(w + 5)$$ 6. **Verify by expansion:** Expanding the factors: $$(w + 3)(w + 5) = w^2 + 5w + 3w + 15 = w^2 + 8w + 15$$ This confirms the factorization is correct. **Final answer:** $$\boxed{(w + 3)(w + 5)}$$