Which of the following is a zero of the polynomial `x^(3) - 8` ?

Options

A. `-2`
B. 2
C. 0
D. `sqrt8`

Answer

To find the zero of the polynomial \( P(x) = x^3 - 8 \), we need to solve the equation \( P(x) = 0 \).

### Step-by-Step Solution:

1. **Set the polynomial equal to zero:**
\[ x^3 - 8 = 0 \]

2. **Isolate \( x^3 \):**
\[ x^3 = 8 \]

3. **Take the cube root of both sides:**
\[ x = \sqrt[3]{8} \]

4. **Calculate the cube root:**
\[ x = 2 \]

5. **Conclusion:**
The zero of the polynomial \( x^3 - 8 \) is \( x = 2 \).

### Verification:

To verify, we can substitute \( x = 2 \) back into the polynomial:

\[ P(2) = 2^3 - 8 = 8 - 8 = 0 \]

Since \( P(2) = 0 \), we confirm that \( x = 2 \) is indeed a zero of the polynomial.