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

Answer

To find the value of \( a \) for which \(-4\) is a zero of the polynomial \( p(x) = x^2 - x - (2a + 2) \), we need to 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 and set it equal to zero:
\[ p(-4) = (-4)^2 - (-4) - (2a + 2) = 0 \]

### Step 2: Simplify the expression
Calculating \( p(-4) \):
\[ p(-4) = 16 + 4 - (2a + 2) \]
\[ p(-4) = 20 - (2a + 2) \]

### Step 3: Set the equation to zero
Now, we set the expression equal to zero:
\[ 20 - (2a + 2) = 0 \]

### Step 4: Solve for \( a \)
Rearranging the equation:
\[ 20 - 2 - 2a = 0 \]
\[ 18 - 2a = 0 \]
Now, isolate \( a \):
\[ 2a = 18 \]
\[ a = \frac{18}{2} = 9 \]

### Conclusion
Thus, the value of \( a \) for which \(-4\) is a zero of the polynomial is:
\[ \boxed{9} \]