In this image, the problem is asking to evaluate $p(5)$, where the polynomial function $p(x) = x^3 + 7x^2 - 20x - 110$ is given. We can use synthetic or direct substitution to calculate $p(5)$.

Given that the long division in the image shows the polynomial being divided by $(x - 5)$, we can conclude that $x = 5$ is a root of the polynomial. This means $p(5) = 0$.

Therefore, $p(5) = 0$.

Would you like more details on how to perform synthetic division or further explanation of polynomial evaluation?

Here are 5 related questions to deepen understanding:

1. How does synthetic division differ from long division for polynomials?
2. Why does the remainder of the division indicate the value of $p(5)$?
3. What does it mean if a number is a root of a polynomial function?
4. How can we factor polynomials after finding a root?
5. How do we use the remainder theorem to evaluate polynomial functions?

Tip: The remainder theorem states that the remainder when a polynomial $p(x)$ is divided by $(x - a)$ is $p(a)$.