If `(x^11+1)` is divided by (x-1) then the remainder is

Options

A. 0
B. 2
C. 1
D. 10

Answer

To find the remainder when \( x^{11} + 1 \) is divided by \( x - 1 \), we can use the Remainder Theorem. The Remainder Theorem states that the remainder of the division of a polynomial \( f(x) \) by \( x - c \) is equal to \( f(c) \).

### Step-by-Step Solution:

1. **Identify the polynomial and the divisor**:
We have the polynomial \( f(x) = x^{11} + 1 \) and we are dividing by \( x - 1 \).

2. **Apply the Remainder Theorem**:
According to the Remainder Theorem, we need to evaluate \( f(1) \) because we are dividing by \( x - 1 \) (where \( c = 1 \)).

3. **Calculate \( f(1) \)**:
\[ f(1) = 1^{11} + 1 \]
\[ = 1 + 1 \]
\[ = 2 \]

4. **State the remainder**:
Therefore, the remainder when \( x^{11} + 1 \) is divided by \( x - 1 \) is \( 2 \).

### Final Answer:
The remainder is \( 2 \).