If `x^(2)+2x-5` is a factor of `x^(4)-2x^(3)+px^(2) +qx-35`, then find the value of `p^(2)-q`.

Explanation

To solve the problem, we need to determine the values of \( p \) and \( q \) such that the polynomial \( x^2 + 2x - 5 \) is a factor of the polynomial \( x^4 - 2x^3 + px^2 + qx - 35 \). We will use polynomial long division to find the values of \( p \) and \( q \).

### Step-by-step Solution:

1. **Set up the long division**: We want to divide \( x^4 - 2x^3 + px^2 + qx - 35 \) by \( x^2 + 2x - 5 \).

2. **Divide the leading terms**: Divide the leading term of the dividend \( x^4 \) by the leading term of the divisor \( x^2 \):
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