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The given function is \( p(x) = x^3 - 10x^2 - 4 \). We are asked to determine the behavior of \( p(x) \) as \( x \) decreases without bound, i.e., as \( x \to -\infty \).

### Step-by-step analysis:

1. **Highest Degree Term (Dominant Term):**
   The term with the highest power of \( x \) is \( x^3 \), which dominates the behavior of the function for large values of \( |x| \). Specifically, for large negative values of \( x \), \( x^3 \) becomes very negative since \( (-x)^3 = -x^3 \) for negative \( x \).

2. **Other Terms:**
   - The \( -10x^2 \) term grows positively (since \( x^2 \) is always positive), but this term is not as strong as \( x^3 \) for large negative \( x \).
   - The constant term \( -4 \) is negligible compared to the dominant \( x^3 \) term as \( x \to -\infty \).

### Conclusion:
As \( x \to -\infty \), the cubic term \( x^3 \) dominates and drives the function \( p(x) \) to decrease without bound. Therefore, the correct answer is:

**A. The output values decrease without bound.**

Would you like further explanation or more details?

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Here are 5 related questions to deepen your understanding:

1. How would the behavior of \( p(x) \) change if the leading term was \( -x^3 \)?
2. How does the behavior of the function change as \( x \to +\infty \)?
3. What effect does the \( -10x^2 \) term have on the behavior of the function at different ranges of \( x \)?
4. How would the function behave if the cubic term was absent?
5. Can you graph \( p(x) = x^3 - 10x^2 - 4 \) and describe its key features (such as intercepts and turning points)?

**Tip:** For polynomial functions, always focus on the highest degree term when analyzing behavior as \( x \to \infty \) or \( x \to -\infty \).

The polynomial function p is given by p(x) = x^3 - 10x^2 - 4. Which of the following describes the behavior of p as the input values decrease without bound?

Understand how to determine the end behavior of the polynomial function p(x) = x^3 - 10x^2 - 4 as the input values decrease without bound. This detailed solution includes an analysis of the dominant term and how it affects the function's output. Ideal for students in Grades 10-12.

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