Find the remainder when `x^(2)-6x+5` is divided by `(x+2)`.

Answer

To find the remainder when \( x^2 - 6x + 5 \) is divided by \( x + 2 \), we can use the Remainder Theorem. According to this theorem, the remainder of a polynomial \( f(x) \) when divided by \( x - c \) is \( f(c) \).

### Step-by-Step Solution:

1. **Identify the polynomial and divisor**:
- The polynomial (dividend) is \( f(x) = x^2 - 6x + 5 \).
- The divisor is \( x + 2 \).

2. **Set the divisor equal to zero**:
- To find the value of \( c \), we set \( x + 2 = 0 \).
- Solving for \( x \) gives us \( x = -2 \).

3. **Substitute \( c \) into the polynomial**:
- We need to evaluate \( f(-2) \):
\[ f(-2) = (-2)^2 - 6(-2) + 5 \]

4. **Calculate \( f(-2) \)**:
- First, calculate \( (-2)^2 \):
\[ (-2)^2 = 4 \]
- Next, calculate \( -6(-2) \):
\[ -6(-2) = 12 \]
- Now, substitute these values back into the equation:
\[ f(-2) = 4 + 12 + 5 \]
- Combine the terms:
\[ f(-2) = 21 \]

5. **Conclusion**:
- The remainder when \( x^2 - 6x + 5 \) is divided by \( x + 2 \) is \( 21 \).

### Final Answer:
The remainder is \( 21 \).