`(x^(2)-7x+15)/(x-3)`, find remainder

Answer

To find the remainder of the polynomial \( f(x) = x^2 - 7x + 15 \) when divided by \( x - 3 \), we can use the Remainder Theorem. According to the theorem, the remainder of the division of a polynomial \( f(x) \) by \( x - a \) is equal to \( f(a) \).

### 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. **Set \( x - 3 = 0 \) to find \( a \):**
- Solve for \( x \):
\[ x - 3 = 0 \implies x = 3 \]
- Here, \( a = 3 \).

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

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

5. **Simplify the expression:**
- Combine the terms:
\[ f(3) = 9 - 21 + 15 = 9 - 6 = 3 \]

6. **Conclusion:**
- The remainder when \( x^2 - 7x + 15 \) is divided by \( x - 3 \) is:
\[ \text{Remainder} = 3 \]

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