The given mathematical problem is:

$(3x^3 - 9x^2 - 5) + (x - 4) = \, ?$

Step-by-step Solution:

1. Group and combine like terms:

   • From $3x^3 - 9x^2 - 5$ and $x - 4$, the terms are:
     • $3x^3$ (no other $x^3$ terms to combine with),
     • $-9x^2$ (no other $x^2$ terms to combine with),
     • $x$ (linear term),
     • Constant terms $-5$ and $-4$.

2. Combine constants: $-5 + (-4) = -9$

3. Write the final expression: $3x^3 - 9x^2 + x - 9$

Final Answer:

$\boxed{3x^3 - 9x^2 + x - 9}$

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Related Questions:

1. How do you simplify polynomials with more variables or terms?
2. What happens if you are adding or subtracting two polynomials with missing terms?
3. Can this polynomial be factored further? If yes, how?
4. How do you graph $3x^3 - 9x^2 + x - 9$?
5. What are the roots (or zeros) of $3x^3 - 9x^2 + x - 9$?

Tip:

When working with polynomials, always organize terms by their degree (highest power of $x$ first) to simplify and clearly identify like terms!