The given polynomial function is:

$p(x) = 7x^3 - 2x^2 + 3x + 10$

We need to evaluate the function at $x = 3$. Substituting $3$ into the function:

$p(3) = 7(3)^3 - 2(3)^2 + 3(3) + 10$

Now, calculating each term:

$p(3) = 7(27) - 2(9) + 3(3) + 10$

$p(3) = 189 - 18 + 9 + 10$

$p(3) = 190$

Thus, $p(3) = 190$.

Would you like more details on this process or have any questions?

Here are 5 related questions for further exploration:

1. How would you evaluate the polynomial at $x = -2$?
2. What is the derivative of the polynomial $p(x)$?
3. How would you find the roots of $p(x) = 0$?
4. What is the degree of the polynomial $p(x)$?
5. What happens to $p(x)$ as $x$ approaches infinity?

Tip: Always follow the order of operations (PEMDAS) when evaluating polynomials or any other expressions.