If `x+2\ ` is a factor of `x^2+m x+14 ,` then `m=`

Options

A. 7
B. 2
C. 9
D. 14

Answer

To solve the problem, we need to find the value of \( m \) such that \( x + 2 \) is a factor of the polynomial \( x^2 + mx + 14 \).

### Step-by-Step Solution:

1. **Understand the Factor Theorem**: According to the Factor Theorem, if \( x + 2 \) is a factor of the polynomial \( P(x) = x^2 + mx + 14 \), then substituting \( x = -2 \) into the polynomial should yield 0.

2. **Substitute \( x = -2 \)**: We will substitute \( x = -2 \) into the polynomial:
\[ P(-2) = (-2)^2 + m(-2) + 14 \]

3. **Calculate \( P(-2) \)**:
\[ P(-2) = 4 - 2m + 14 \]
Simplifying this gives:
\[ P(-2) = 18 - 2m \]

4. **Set the Polynomial Equal to Zero**: Since \( x + 2 \) is a factor, we set \( P(-2) = 0 \):
\[ 18 - 2m = 0 \]

5. **Solve for \( m \)**:
\[ 18 = 2m \]
Dividing both sides by 2:
\[ m = \frac{18}{2} = 9 \]

### Conclusion:
The value of \( m \) is \( 9 \).