If `x^(2) - 3x + 2` is factor of `x^(4) - px^(2) + q` then `2q - p` is equal to

Explanation

To solve the problem, we need to determine the values of \( p \) and \( q \) such that \( x^2 - 3x + 2 \) is a factor of \( x^4 - px^2 + q \).

### Step-by-step Solution:

1. **Identify the Factor**:
The polynomial \( x^2 - 3x + 2 \) can be factored as:
\[ x^2 - 3x + 2 = (x - 1)(x - 2) \]
This means that the roots of this polynomial are \( x = 1 \) and \( x = 2 \).

2. **Substitute the Roots into the Polynomial**:
Since \( x^2 - 3x + 2 \) is a factor of \( x^4 - px^2 + q \), both \( x = 1 \) and \( x = 2 \) must satisfy the equation \( x^4 - px^2 + q = 0 \).

3. **Substituting \( x = 1 \)**:
Substitute \( x = 1 \) into the polynomial:
\[ 1^4 - p(1^2) + q = 0 \implies 1 - p + q = 0 \implies q = p - 1 \quad \text{(Equation 1)} \]

4. **Substituting \( x = 2 \)**:
Substitute \( x = 2 \) into the polynomial:
\[ 2^4 - p(2^2) + q = 0 \implies 16 - 4p + q = 0 \implies q = 4p - 16 \quad \text{(Equation 2)} \]

5. **Set the Two Equations for \( q \) Equal**:
From Equation 1 and Equation 2, we have:
\[ p - 1 = 4p - 16 \]

6. **Solve for \( p \)**:
Rearranging gives:
\[ -1 + 16 = 4p - p \implies 15 = 3p \implies p = 5 \]

7. **Substitute \( p \) back to find \( q \)**:
Substitute \( p = 5 \) into Equation 1:
\[ q = 5 - 1 = 4 \]

8. **Calculate \( 2q - p \)**:
Now we need to find \( 2q - p \):
\[ 2q - p = 2(4) - 5 = 8 - 5 = 3 \]

### Final Answer:
Thus, the value of \( 2q - p \) is \( \boxed{3} \).