If x = 11, the value of `x^5 - 12 x^4 + 12x^3 - 12x^2 + 12x -1` is

Options

A. 11
B. 10
C. 12
D. `-10`

Answer

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

### Step 1: Substitute the value of \( x \)
We start by substituting \( x = 11 \) into the expression:

\[ 11^5 - 12 \cdot 11^4 + 12 \cdot 11^3 - 12 \cdot 11^2 + 12 \cdot 11 - 1 \]

### Step 2: Calculate each power of 11
Now we need to calculate the powers of 11:

- \( 11^2 = 121 \)
- \( 11^3 = 11 \times 121 = 1331 \)
- \( 11^4 = 11 \times 1331 = 14641 \)
- \( 11^5 = 11 \times 14641 = 161051 \)

### Step 3: Substitute the calculated values
Now we can substitute these values back into the expression:

\[ 161051 - 12 \cdot 14641 + 12 \cdot 1331 - 12 \cdot 121 + 12 \cdot 11 - 1 \]

### Step 4: Calculate the products
Next, we calculate the products:

- \( 12 \cdot 14641 = 175692 \)
- \( 12 \cdot 1331 = 15972 \)
- \( 12 \cdot 121 = 1452 \)
- \( 12 \cdot 11 = 132 \)

### Step 5: Substitute the products into the expression
Now we substitute these products into the expression:

\[ 161051 - 175692 + 15972 - 1452 + 132 - 1 \]

### Step 6: Simplify the expression
Now we simplify step by step:

1. \( 161051 - 175692 = -14641 \)
2. \( -14641 + 15972 = 1331 \)
3. \( 1331 - 1452 = -121 \)
4. \( -121 + 132 = 11 \)
5. \( 11 - 1 = 10 \)

### Final Answer
Thus, the value of the expression when \( x = 11 \) is:

\[ \boxed{10} \]