When `(p^(2)-p-29)` is divided by `(p-6)` the remainder is 1.

Answer

To solve the problem, we will use the Remainder Theorem, which states that when a polynomial \( f(p) \) is divided by \( p - a \), the remainder is \( f(a) \).

### Step-by-step Solution:

1. **Identify the polynomial and the divisor**:
- The polynomial is \( f(p) = p^2 - p - 29 \).
- The divisor is \( p - 6 \).

2. **Apply the Remainder Theorem**:
- According to the Remainder Theorem, we need to evaluate \( f(6) \) to find the remainder when \( f(p) \) is divided by \( p - 6 \).

3. **Substitute \( p = 6 \) into the polynomial**:
\[ f(6) = 6^2 - 6 - 29 \]

4. **Calculate \( 6^2 \)**:
\[ 6^2 = 36 \]

5. **Substitute back into the equation**:
\[ f(6) = 36 - 6 - 29 \]

6. **Perform the subtraction**:
- First, calculate \( 36 - 6 \):
\[ 36 - 6 = 30 \]
- Then, subtract 29 from 30:
\[ 30 - 29 = 1 \]

7. **Conclusion**:
- The remainder when \( p^2 - p - 29 \) is divided by \( p - 6 \) is \( 1 \).

### Final Answer:
When \( p^2 - p - 29 \) is divided by \( p - 6 \), the remainder is indeed \( 1 \).

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