The sum of $8x - 2$ and $-3x^2 - 7$ can be found by combining like terms. Here's the step-by-step process:

1. Write the expression: $(8x - 2) + (-3x^2 - 7)$

2. Distribute the plus sign (which doesn't change anything in this case): $8x - 2 - 3x^2 - 7$

3. Combine like terms:

   • There's only one $x^2$ term: $-3x^2$.
   • The $x$-term is $8x$.
   • The constants are $-2$ and $-7$, which sum to $-9$.

Thus, the result is: $-3x^2 + 8x - 9$

So, the sum of $8x - 2$ and $-3x^2 - 7$ is $-3x^2 + 8x - 9$.

Would you like further clarification or more details on this? Here are five related questions:

1. How do you add polynomials with more than one variable?
2. Can you subtract these two expressions and see the result?
3. What happens if we multiply $8x - 2$ and $-3x^2 - 7$?
4. How do you factor quadratic expressions like $-3x^2 + 8x - 9$?
5. Can you find the roots of $-3x^2 + 8x - 9 = 0$ using the quadratic formula?

Tip: Always align like terms when adding or subtracting polynomials to simplify the process.