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The given function is:

\[
p(x) = \frac{x^2 - 4}{2x + 1}
\]

You are asked to find \( p(-8) \), which means substituting \( x = -8 \) into the function.

Let's compute it step-by-step:

\[
p(-8) = \frac{(-8)^2 - 4}{2(-8) + 1}
\]

1. First, calculate \( (-8)^2 - 4 \):
   \[
   (-8)^2 = 64, \quad 64 - 4 = 60
   \]

2. Next, calculate \( 2(-8) + 1 \):
   \[
   2(-8) = -16, \quad -16 + 1 = -15
   \]

3. Now, substitute these values into the equation:
   \[
   p(-8) = \frac{60}{-15} = -4
   \]

Thus, \( p(-8) = -4 \).

Would you like more details on any step?

Here are 5 follow-up questions you might consider:
1. What is the domain of \( p(x) \)?
2. How do you find the vertical asymptotes of this rational function?
3. Can you simplify \( \frac{x^2 - 4}{2x + 1} \) by factoring?
4. What is the behavior of \( p(x) \) as \( x \to \infty \)?
5. What would \( p(x) \) be if you change the numerator to \( x^2 + 4 \)?

**Tip:** When evaluating a rational function, always check whether the denominator is zero at the substitution point to avoid undefined values.

Learn how to evaluate the rational function p(x) = (x^2 - 4) / (2x + 1) at x = -8, with a detailed step-by-step solution. This problem covers key algebraic concepts including substitution and simplifying rational expressions. Suitable for students in Grades 9-12.

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