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Let's solve the expression:

\[
(2x^2 - 5x - x^3) - (x^2 - 4x - 3)
\]

### Step 1: Distribute the negative sign
When subtracting, we distribute the negative sign to all the terms inside the second parentheses:

\[
= (2x^2 - 5x - x^3) - x^2 + 4x + 3
\]

### Step 2: Combine like terms
Now, let's combine the like terms:

- \(x^3\) terms: \(-x^3\)
- \(x^2\) terms: \(2x^2 - x^2 = x^2\)
- \(x\) terms: \(-5x + 4x = -x\)
- Constant terms: \(3\)

Thus, the expression simplifies to:

\[
-x^3 + x^2 - x + 3
\]

### Final Answer:
The correct answer is **option b**: \(x^3 + x^2 - x + 3\).

Would you like further clarification or more details?

Here are 5 related questions:
1. How do you distribute negative signs in more complex expressions?
2. How do you simplify expressions with higher-order polynomials?
3. What are the common mistakes when simplifying expressions with multiple variables?
4. How do you handle polynomials when adding or subtracting them?
5. How can factoring help in solving polynomial equations?

**Tip:** Always double-check for the correct distribution of negative signs, as small errors in this step can lead to incorrect results.

Learn how to solve the polynomial expression (2x^2 - 5x - x^3) - (x^2 - 4x - 3) with a step-by-step solution. This algebraic problem demonstrates how to use the distributive property and combine like terms. Ideal for students in Grades 9-11.

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