When number `x^2 + 7x + 15` is divided by (x - 5), the remainder will be?

Options

A. 25
B. 30
C. 75
D. 45

Answer

To find the remainder when the polynomial \( x^2 + 7x + 15 \) is divided by \( x - 5 \), we can use the Remainder Theorem. According to the Remainder 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 \( x - 5 \), which means \( c = 5 \).

2. **Evaluate the polynomial at \( c = 5 \)**:
- Substitute \( x = 5 \) into the polynomial:
\[ f(5) = (5)^2 + 7(5) + 15 \]

3. **Calculate \( f(5) \)**:
- Calculate \( (5)^2 \):
\[ (5)^2 = 25 \]
- Calculate \( 7(5) \):
\[ 7(5) = 35 \]
- Now add these values together with 15:
\[ f(5) = 25 + 35 + 15 \]

4. **Perform the addition**:
- First, add \( 25 + 35 \):
\[ 25 + 35 = 60 \]
- Now add \( 60 + 15 \):
\[ 60 + 15 = 75 \]

5. **Conclusion**:
- The remainder when \( x^2 + 7x + 15 \) is divided by \( x - 5 \) is \( 75 \).

### Final Answer:
The remainder is \( 75 \).

---