If -4 is a zero of the polynomial `x^(2)-x-(2k+2)`, then find the value of k.

Explanation

To find the value of \( k \) given that \(-4\) is a zero of the polynomial \( x^2 - x - (2k + 2) \), we can follow these steps:

### Step 1: Substitute \(-4\) into the polynomial
Since \(-4\) is a zero of the polynomial, we can substitute \( x = -4 \) into the polynomial equation:
\[ (-4)^2 - (-4) - (2k + 2) = 0 \]

### Step 2: Simplify the equation
Now, calculate each term:
\[ 16 + 4 - (2k + 2) = 0 \]
This simplifies to:
\[ 20 - (2k + 2) = 0 \]

### Step 3: Rearrange the equation
Now, distribute the negative sign:
\[ 20 - 2k - 2 = 0 \]
This simplifies to:
\[ 18 - 2k = 0 \]

### Step 4: Solve for \( k \)
Now, isolate \( k \):
\[ 2k = 18 \]
Dividing both sides by 2 gives:
\[ k = 9 \]

### Final Answer
The value of \( k \) is \( 9 \).

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