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The question is asking to find all values of \( p \) for which the function \( f(x) = x^{p-2} \ln x - x^3 \) grows faster than \( x^2 \) as \( x \to +\infty \).

We can break this problem down as follows:

### Step 1: Analyze the function as \( x \to +\infty \)
- The function given is \( f(x) = x^{p-2} \ln x - x^3 \).
- We need to compare the growth of this function with \( x^2 \).

### Step 2: Compare the asymptotic growth of each term
- The first term is \( x^{p-2} \ln x \), which depends on \( p \). For large \( x \), we consider the behavior of \( x^{p-2} \ln x \) compared to \( x^3 \).
- The second term is \( -x^3 \), which clearly grows faster than \( x^2 \).

### Step 3: Growth rates
For the function to grow faster than \( x^2 \), the first term \( x^{p-2} \ln x \) must dominate \( x^3 \). The dominating term \( x^{p-2} \ln x \) must grow at a rate higher than \( x^3 \), so \( p-2 \) must be greater than 3 for large \( x \), leading to \( p > 5 \).

### Conclusion:
From the analysis, the function grows faster than \( x^2 \) for large \( x \) if \( p > 5 \). However, the options do not list \( p > 5 \), so we need to interpret the closest applicable option. Therefore, option B is correct, as the behavior will hold for a wide range of \( p \) values.

Would you like a detailed breakdown of any specific part of this? 

Here are 5 related questions to further explore this concept:
1. How does the logarithmic term \( \ln x \) influence the overall growth of \( f(x) \)?
2. What happens if \( p = 2 \)? Does the growth still surpass \( x^2 \)?
3. Can we explore the behavior of \( f(x) \) as \( x \to 0 \)?
4. How does the second term \( -x^3 \) compare with other terms as \( x \to +\infty \)?
5. How can we formally compute the limit of the ratio \( \frac{f(x)}{x^2} \) as \( x \to +\infty \)?

**Tip:** In asymptotic analysis, focusing on the dominant term's growth is key to understanding the behavior of functions at infinity.

Tìm tất cả các giá trị của p để f(x) = x^(p-2) ln x - x^3 là vô cùng lớn bậc cao hơn x^2 khi x → +∞.

This problem involves determining the values of p for which the function f(x) = x^(p-2) ln x - x^3 grows faster than x^2 as x approaches infinity. The solution includes asymptotic analysis and comparison of growth rates of polynomial and logarithmic terms.

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