find the value of the expression ` x^5 - 12 x^4 +12x^3 - 12 x^2 +12 x -1` when x =11 .

Options

A. 12
B. 0
C. 10
D. 11

Answer

To find the value of the expression \( x^5 - 12x^4 + 12x^3 - 12x^2 + 12x - 1 \) when \( x = 11 \), we can follow these steps:

1. **Substitute \( x = 11 \)** into the expression:
\[ 11^5 - 12 \cdot 11^4 + 12 \cdot 11^3 - 12 \cdot 11^2 + 12 \cdot 11 - 1 \]

2. **Calculate each power of 11**:
- \( 11^2 = 121 \)
- \( 11^3 = 11 \cdot 121 = 1331 \)
- \( 11^4 = 11 \cdot 1331 = 14641 \)
- \( 11^5 = 11 \cdot 14641 = 161051 \)

3. **Substitute these values back into the expression**:
\[ 161051 - 12 \cdot 14641 + 12 \cdot 1331 - 12 \cdot 121 + 12 \cdot 11 - 1 \]

4. **Calculate the products**:
- \( 12 \cdot 14641 = 175692 \)
- \( 12 \cdot 1331 = 15972 \)
- \( 12 \cdot 121 = 1452 \)
- \( 12 \cdot 11 = 132 \)

5. **Substitute these products back into the expression**:
\[ 161051 - 175692 + 15972 - 1452 + 132 - 1 \]

6. **Perform the calculations step by step**:
- First, calculate \( 161051 - 175692 \):
\[ 161051 - 175692 = -14641 \]
- Next, add \( 15972 \):
\[ -14641 + 15972 = 1331 \]
- Then, subtract \( 1452 \):
\[ 1331 - 1452 = -121 \]
- Add \( 132 \):
\[ -121 + 132 = 11 \]
- Finally, subtract \( 1 \):
\[ 11 - 1 = 10 \]

7. **Final result**:
The value of the expression when \( x = 11 \) is \( 10 \).