To solve the inequality \(x^3 - 4x^2 - 11x + 60 > 0\), we need to follow these steps:

### 1. **Find the roots of the cubic equation**:
   First, solve the equation \(x^3 - 4x^2 - 11x + 60 = 0\). The roots of this equation will help us determine the intervals where the inequality might change its sign.

### 2. **Factor the cubic equation**:
   We can use trial and error, synthetic division, or other factoring methods to find the roots.

Let's find the roots by trial and error using the Rational Root Theorem, which suggests possible rational roots based on the factors of the constant term \(60\) and the leading coefficient \(1\).

### 3. **Check potential roots**:
   - \(x = 2\):  
     \[
     2^3 - 4(2)^2 - 11(2) + 60 = 8 - 16 - 22 + 60 = 30 \quad \text{(Not a root)}
     \]
  

Learn how to solve the cubic inequality x^3 - 4x^2 - 11x + 60 > 0 with a detailed step-by-step solution. This problem involves solving cubic equations and applying the Rational Root Theorem. Suitable for advanced high school students in Grades 11-12.

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