Under tree plantation programme students of Class IX planted total `(3x^(2)-4x-4)` trees in school.
If total number of students is the class (x-2) then find out number of tree planted by each students. (Assuing each students planted equal number of trees).

Answer

To find the number of trees planted by each student, we need to divide the total number of trees by the total number of students. Let's go through the steps to solve the problem.

### Step-by-Step Solution:

1. **Identify the total number of trees and students:**
- Total trees planted = \(3x^2 - 4x - 4\)
- Total students = \(x - 2\)

2. **Set up the division:**
- We need to divide the total number of trees by the total number of students:
\[ \text{Number of trees planted by each student} = \frac{3x^2 - 4x - 4}{x - 2} \]

3. **Perform polynomial long division:**
- Divide \(3x^2\) by \(x\) to get \(3x\).
- Multiply \(3x\) by \(x - 2\):
\[ 3x \cdot (x - 2) = 3x^2 - 6x \]
- Subtract this from \(3x^2 - 4x - 4\):
\[ (3x^2 - 4x - 4) - (3x^2 - 6x) = -4x + 6x - 4 = 2x - 4 \]

4. **Continue the division:**
- Now divide \(2x\) by \(x\) to get \(2\).
- Multiply \(2\) by \(x - 2\):
\[ 2 \cdot (x - 2) = 2x - 4 \]
- Subtract this from \(2x - 4\):
\[ (2x - 4) - (2x - 4) = 0 \]

5. **Conclusion:**
- Since the remainder is \(0\), the division is exact.
- Therefore, the number of trees planted by each student is:
\[ 3x + 2 \]

### Final Answer:
The number of trees planted by each student is \(3x + 2\).

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