If `x= -3`, then what is the value of `x^(4)-x^(3)-x^(2)+3`?

Answer

To solve the expression \( x^4 - x^3 - x^2 + 3 \) for \( x = -3 \), we will substitute \(-3\) into the expression and simplify step by step.

### Step-by-Step Solution:

1. **Substitute \( x = -3 \)**:
\[ (-3)^4 - (-3)^3 - (-3)^2 + 3 \]

2. **Calculate \( (-3)^4 \)**:
\[ (-3)^4 = 81 \quad \text{(since } 3^4 = 81\text{)} \]

3. **Calculate \( -(-3)^3 \)**:
\[ (-3)^3 = -27 \quad \text{(since } 3^3 = 27\text{)} \]
Therefore,
\[ -(-3)^3 = 27 \]

4. **Calculate \( -(-3)^2 \)**:
\[ (-3)^2 = 9 \quad \text{(since } 3^2 = 9\text{)} \]
Therefore,
\[ -(-3)^2 = -9 \]

5. **Combine all the calculated values**:
\[ 81 + 27 - 9 + 3 \]

6. **Perform the addition and subtraction**:
- First, add \( 81 + 27 = 108 \)
- Then, subtract \( 9 \): \( 108 - 9 = 99 \)
- Finally, add \( 3 \): \( 99 + 3 = 102 \)

Thus, the value of \( x^4 - x^3 - x^2 + 3 \) when \( x = -3 \) is \( \boxed{102} \).