https://file.aiquickdraw.com/mathbot/file/17272802210091u7gd1gw.jpg

Let's work through the given polynomial:

### Polynomial:  
\[
-x^3 - 4x^2 - 5x
\]

We can factor this step by step.

1. **Factor out the greatest common factor (GCF):**  
   The GCF of all terms is \(-x\), so we can factor out \(-x\) from the polynomial:
   \[
   -x(x^2 + 4x + 5)
   \]

So the factored form is:
\[
-x(x^2 + 4x + 5)
\]

Now, let's compare this with the given answer options:
- **Option A:** \(-x(x^2 + 4x - 5)\) – Incorrect.
- **Option B:** \(x(x^2 + 4x + 5)\) – Incorrect.
- **Option C:** \(-x(x^2 + 4x + 5)\) – Correct.
- **Option D:** \(-x(x^2 - 4x - 5)\) – Incorrect.

Thus, the correct answer is **C**:  
\[
-x(x^2 + 4x + 5)
\]

Would you like further details or have any additional questions?

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Here are 5 related questions:
1. How do you determine the greatest common factor (GCF) in a polynomial?
2. Can the quadratic part \((x^2 + 4x + 5)\) be factored further?
3. How do you handle negative leading coefficients in polynomials during factoring?
4. What is the difference between factoring completely and partially factoring a polynomial?
5. How can factoring help in solving polynomial equations?

**Tip:** Always check if you can factor out a negative sign when the leading term in a polynomial has a negative coefficient.

Learn how to factor the polynomial -x^3 - 4x^2 - 5x by factoring out the greatest common factor (GCF). This problem includes detailed explanations of the factoring process and is ideal for students in Grades 8-10.

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