Given the polynomial function:

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

We want to evaluate the function at $x = -3$.

Substitute $x = -3$ into the polynomial:

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

Now calculate each term step by step:

1. $(-3)^3 = -27$, so $7(-3)^3 = 7 \times -27 = -189$
2. $(-3)^2 = 9$, so $-2(-3)^2 = -2 \times 9 = -18$
3. $3(-3) = 3 \times -3 = -9$
4. The constant term is $10$

Now sum up all the terms:

$p(-3) = -189 - 18 - 9 + 10$ $p(-3) = -206$

Thus, $p(-3) = -206$.

Would you like further details or have any questions?

Here are 5 related questions for deeper exploration:

1. What is the degree of the polynomial function $p(x)$?
2. How do you find the roots of the polynomial function $p(x)$?
3. What is the derivative of $p(x)$?
4. Can you factor the polynomial $p(x)$?
5. What is the behavior of $p(x)$ as $x$ approaches infinity?

Tip: When substituting negative numbers into polynomial functions, be careful with the signs, especially with powers of negative numbers.