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!