You want to simplify the expression \((x^2 + 8x + 15) \div (x + 3)\).

### Steps to solve:

1. **Factor the numerator**: We need to factor \(x^2 + 8x + 15\). 
   - We find two numbers that multiply to give \(15\) and add to give \(8\). These numbers are \(3\) and \(5\).
   - So, \(x^2 + 8x + 15 = (x + 3)(x + 5)\).

2. **Rewrite the expression**: Now the expression becomes:
   \[
   \frac{(x + 3)(x + 5)}{x + 3}
   \]

3. **Simplify**: Since \((x + 3)\) appears in both the numerator and denominator, we can cancel it out (as long as \(x \neq -3\) to avoid division by zero):
   \[
   (x + 5)
   \]

### Final Answer:
\[
x + 5 \quad \text{for} \quad x \neq -3
\]

Would you like further clarification or details?

Here are 5 related questions to explore:
1. How do you factor quadratic expressions like \(x^2 + 8x + 15\)?
2. What are the conditions for canceling terms in rational expressions?
3. What happens if \(x = -3\) in this problem?
4. How do you solve polynomial division when the numerator doesn’t factor nicely?
5. How would you handle higher-degree polynomials in the numerator?

**Tip:** Always check for restrictions on the variable when canceling terms, as this ensures you don’t divide by zero!

Learn how to simplify the expression (x² + 8x + 15) ÷ (x + 3) using quadratic factorization and rational expression simplification. This problem demonstrates factoring and canceling techniques, suitable for students in Grades 8-10.

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