If one of the factors of `(x ^(2) + kx + 12)` is (x + 3), then find the value of k.

Options

A. 8
B. 7
C. 6
D. 5

Answer

To find the value of \( k \) such that one of the factors of \( x^2 + kx + 12 \) is \( (x + 3) \), we can follow these steps:

### Step 1: Set up the equation
Since \( (x + 3) \) is a factor, we can substitute \( x = -3 \) into the polynomial \( x^2 + kx + 12 \) and set it equal to zero:
\[ (-3)^2 + k(-3) + 12 = 0 \]

### Step 2: Simplify the equation
Calculating \( (-3)^2 \):
\[ 9 + k(-3) + 12 = 0 \]
This simplifies to:
\[ 9 - 3k + 12 = 0 \]

### Step 3: Combine like terms
Now combine the constants:
\[ 21 - 3k = 0 \]

### Step 4: Solve for \( k \)
To isolate \( k \), we can rearrange the equation:
\[ -3k = -21 \]
Dividing both sides by -3 gives:
\[ k = \frac{21}{3} = 7 \]

### Conclusion
Thus, the value of \( k \) is:
\[ \boxed{7} \]