To add the polynomials $(8x^2 - 8x + 5)$ and $(3x^3 - 3x)$, we simply combine the like terms.

Let's break it down:

1. Start with the highest degree terms:

   • $3x^3$ is the only cubic term, so it stays as is.

2. Next, combine the quadratic terms:

   • The only quadratic term is $8x^2$.

3. Now, the linear terms:

   • $-8x$ and $-3x$ combine to give $-11x$.

4. Finally, the constant term:

   • $+5$ is the only constant, so it stays as is.

Thus, the sum of the polynomials is: $3x^3 + 8x^2 - 11x + 5$

Would you like any further clarification on this process or additional help with polynomials?

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Here are five related questions to explore:

1. How do we subtract polynomials?
2. What happens when we multiply polynomials with different degrees?
3. How do we factor polynomials like the one above?
4. What is the degree of a polynomial, and how does it affect its behavior?
5. How do we perform synthetic division on polynomials?

Tip: Always organize polynomials by their degree before adding or subtracting to make combining like terms easier!