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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.

Let A = 3x^3 + x - 5, B = x^2 - x - 5x^3, and C = x^2 - 5 + 8x^3. When simplified, the expression (A + B) - C is:

Learn how to simplify the polynomial expression (A + B) - C where A = 3x^3 + x - 5, B = x^2 - x - 5x^3, and C = x^2 - 5 + 8x^3. This detailed solution explains how to add and subtract polynomials, group like terms, and determine the degree of the final polynomial. Suitable for Grades 9-10.

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