If ( -1) is a zero of the polynomial `p(x) = x^2 - 7x -8`, then the other zero is:

Options

A. `-8`
B. `-7`
C. 1
D. 8

Answer

To find the other zero of the polynomial \( p(x) = x^2 - 7x - 8 \) given that one zero is \( -1 \), we can follow these steps:

### Step 1: Use the fact that \( -1 \) is a zero of the polynomial
Since \( -1 \) is a zero, we know that:
\[ p(-1) = 0 \]
This means that when we substitute \( x = -1 \) into the polynomial, the result should be zero.

### Step 2: Write the polynomial in standard form
The polynomial is already in standard form:
\[ p(x) = x^2 - 7x - 8 \]

### Step 3: Use the relationship between the roots
For a quadratic polynomial \( ax^2 + bx + c \), if \( \alpha \) and \( \beta \) are the roots, then:
\[ \alpha + \beta = -\frac{b}{a} \]
In our case, \( a = 1 \), \( b = -7 \), and \( c = -8 \). Therefore:
\[ \alpha + \beta = -\frac{-7}{1} = 7 \]
Since we know one root \( \alpha = -1 \), we can find the other root \( \beta \) using:
\[ -1 + \beta = 7 \]

### Step 4: Solve for the other zero
Rearranging the equation gives:
\[ \beta = 7 + 1 = 8 \]

### Conclusion
Thus, the other zero of the polynomial \( p(x) = x^2 - 7x - 8 \) is:
\[ \boxed{8} \]