If ` p(x)=x^(2)-2sqrt(2)x+1` , then p `(2sqrt(2))` is equal to

Options

A. 0
B. 1
C. `4sqrt(2)`
D. `8sqrt(2)+1`

Explanation

To find \( p(2\sqrt{2}) \) for the polynomial \( p(x) = x^2 - 2\sqrt{2}x + 1 \), we will substitute \( x \) with \( 2\sqrt{2} \) in the polynomial and simplify step by step.

### Step-by-Step Solution:

1. **Substitute \( x \) with \( 2\sqrt{2} \)**:
\[ p(2\sqrt{2}) = (2\sqrt{2})^2 - 2\sqrt{2}(2\sqrt{2}) + 1 \]

**Hint**: Remember to square the term \( 2\sqrt{2} \) carefully.

2. **Calculate \( (2\sqrt{2})^2 \)**:
\[ (2\sqrt{2})^2 = 2^2 \cdot (\sqrt{2})^2 = 4 \cdot 2 = 8 \]

**Hint**: Use the property \( (a\sqrt{b})^2 = a^2 \cdot b \).

3. **Calculate \( -2\sqrt{2}(2\sqrt{2}) \)**:
\[ -2\sqrt{2}(2\sqrt{2}) = -4 \cdot (\sqrt{2} \cdot \sqrt{2}) = -4 \cdot 2 = -8 \]

**Hint**: Multiply the coefficients and remember that \( \sqrt{2} \cdot \sqrt{2} = 2 \).

4. **Combine the results**:
\[ p(2\sqrt{2}) = 8 - 8 + 1 \]

**Hint**: Keep track of positive and negative signs while combining.

5. **Simplify the expression**:
\[ p(2\sqrt{2}) = 0 + 1 = 1 \]

**Hint**: Adding zero to a number does not change its value.

### Final Answer:
Thus, \( p(2\sqrt{2}) = 1 \).