The question asks for the simplification of the expression $(A + B) - C$, where:

• $A = 3x^3 + x - 5$,
• $B = x^2 - x - 5x^3$,
• $C = x^2 - 5 + 8x^3$.

Step 1: Add $A$ and $B$:

$A + B = (3x^3 + x - 5) + (x^2 - x - 5x^3)$ Combine like terms: $A + B = (3x^3 - 5x^3) + x^2 + (x - x) - 5 = -2x^3 + x^2 - 5$

Step 2: Subtract $C$ from $A + B$:

$(A + B) - C = (-2x^3 + x^2 - 5) - (x^2 - 5 + 8x^3)$ Distribute the negative sign: $(A + B) - C = -2x^3 + x^2 - 5 - x^2 + 5 - 8x^3$ Combine like terms: $(A + B) - C = (-2x^3 - 8x^3) + (x^2 - x^2) + (-5 + 5) = -10x^3$

Final Expression:

$(A + B) - C = -10x^3$

This is a monomial of degree 3, which matches the fourth option.

Would you like any more details on this? Here are some related questions to deepen your understanding:

1. What is the degree of a polynomial, and how is it determined?
2. How do you combine like terms in polynomial expressions?
3. What are the rules for subtracting polynomials?
4. Can a monomial be of any degree, and how do you classify it?
5. How do you solve similar problems with more variables or higher degrees?

Tip: Always group like terms carefully when adding or subtracting polynomials to avoid errors.