When `x^2 - 7x + 15` is divided by (x - 3), the remainder obtained is ?

Options

A. 3
B. 1
C. 0
D. 2

Answer

To find the remainder when the polynomial \( x^2 - 7x + 15 \) is divided by \( x - 3 \), we can use the Remainder Theorem. According to this theorem, 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**:
- The polynomial is \( f(x) = x^2 - 7x + 15 \).
- The divisor is \( x - 3 \).

2. **Apply the Remainder Theorem**:
- According to the Remainder Theorem, we need to evaluate \( f(3) \) because we are dividing by \( x - 3 \).

3. **Substitute \( x = 3 \) into the Polynomial**:
\[ f(3) = 3^2 - 7 \cdot 3 + 15 \]

4. **Calculate \( f(3) \)**:
- First, calculate \( 3^2 \):
\[ 3^2 = 9 \]
- Next, calculate \( -7 \cdot 3 \):
\[ -7 \cdot 3 = -21 \]
- Now substitute these values into the equation:
\[ f(3) = 9 - 21 + 15 \]
- Combine the terms:
\[ 9 - 21 = -12 \]
\[ -12 + 15 = 3 \]

5. **Conclusion**:
- The remainder when \( x^2 - 7x + 15 \) is divided by \( x - 3 \) is \( 3 \).

### Final Answer:
The remainder is \( 3 \).