For what value of k is -4 a zero of the polynomial `f(x)=x^2-x-(2k+2)`?

Options

A. 7
B. 1
C. 9
D. 4

Answer

To find the value of \( k \) for which \(-4\) is a zero of the polynomial \( f(x) = x^2 - x - (2k + 2) \), we need to substitute \(-4\) into the polynomial and set it equal to zero.

### Step-by-Step Solution:

1. **Substitute \(-4\) into the polynomial**:
\[ f(-4) = (-4)^2 - (-4) - (2k + 2) \]

2. **Calculate \((-4)^2\)**:
\[ (-4)^2 = 16 \]

3. **Calculate \(-(-4)\)**:
\[ -(-4) = 4 \]

4. **Combine the results**:
\[ f(-4) = 16 + 4 - (2k + 2) \]

5. **Simplify the expression**:
\[ f(-4) = 20 - (2k + 2) \]
\[ f(-4) = 20 - 2k - 2 \]
\[ f(-4) = 18 - 2k \]

6. **Set the polynomial equal to zero** (since \(-4\) is a zero):
\[ 18 - 2k = 0 \]

7. **Solve for \( k \)**:
\[ 18 = 2k \]
\[ k = \frac{18}{2} = 9 \]

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