Which of the following is not a zero of the polynomial
`p(x) = x^(3) - 7x + 6`

Options

A. 1
B. 2
C. `-2`
D. `-3`

Answer

To determine which of the following is not a zero of the polynomial \( p(x) = x^3 - 7x + 6 \), we will evaluate the polynomial at different values (potential roots) and check which one does not yield zero.

### Step-by-Step Solution:

1. **Identify the Polynomial**:
The polynomial given is:
\[ p(x) = x^3 - 7x + 6 \]

2. **Test the First Value (1)**:
Substitute \( x = 1 \) into the polynomial:
\[ p(1) = 1^3 - 7 \cdot 1 + 6 = 1 - 7 + 6 = 0 \]
Since \( p(1) = 0 \), \( 1 \) is a zero of the polynomial.

3. **Test the Second Value (2)**:
Substitute \( x = 2 \) into the polynomial:
\[ p(2) = 2^3 - 7 \cdot 2 + 6 = 8 - 14 + 6 = 0 \]
Since \( p(2) = 0 \), \( 2 \) is also a zero of the polynomial.

4. **Test the Third Value (-2)**:
Substitute \( x = -2 \) into the polynomial:
\[ p(-2) = (-2)^3 - 7 \cdot (-2) + 6 = -8 + 14 + 6 = 12 \]
Since \( p(-2) = 12 \neq 0 \), \( -2 \) is not a zero of the polynomial.

5. **Test the Fourth Value (-3)**:
Substitute \( x = -3 \) into the polynomial:
\[ p(-3) = (-3)^3 - 7 \cdot (-3) + 6 = -27 + 21 + 6 = 0 \]
Since \( p(-3) = 0 \), \( -3 \) is a zero of the polynomial.

### Conclusion:
From the evaluations, we find:
- \( 1 \) is a zero.
- \( 2 \) is a zero.
- \( -2 \) is **not** a zero.
- \( -3 \) is a zero.

Thus, the answer is that **-2 is not a zero of the polynomial** \( p(x) = x^3 - 7x + 6 \).