If `x-4` is a factor of `x^(2)-kx+2k`, where k is a constant, what is the value of k?

Options

A. `-4`
B. `4`
C. `8`
D. `12`

Explanation

To find the value of \( k \) such that \( x - 4 \) is a factor of the quadratic equation \( x^2 - kx + 2k \), we can follow these steps:

### Step 1: Set up the equation
Since \( x - 4 \) is a factor, substituting \( x = 4 \) into the quadratic equation should yield zero:
\[ x^2 - kx + 2k = 0 \]

### Step 2: Substitute \( x = 4 \)
Substituting \( x = 4 \) into the equation gives:
\[ 4^2 - k(4) + 2k = 0 \]

### Step 3: Simplify the equation
Calculating \( 4^2 \):
\[ 16 - 4k + 2k = 0 \]
This simplifies to:
\[ 16 - 2k = 0 \]

### Step 4: Solve for \( k \)
Now, we can isolate \( k \):
\[ 16 = 2k \]
Dividing both sides by 2:
\[ k = 8 \]

### Conclusion
Thus, the value of \( k \) is \( 8 \).

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