What must be added to `x^4+2x^3-2x^2+x-1` so that the result is exactly divisible by `x^2+2x-3.`

Explanation

To solve the problem of finding what must be added to the polynomial \( P(x) = x^4 + 2x^3 - 2x^2 + x - 1 \) so that it becomes exactly divisible by \( D(x) = x^2 + 2x - 3 \), we can follow these steps:

### Step 1: Perform Polynomial Long Division
We will divide \( P(x) \) by \( D(x) \).

1. **Divide the leading term**: Divide the leading term of \( P(x) \) (which is \( x^4 \)) by the leading term of \( D(x) \) (which is \( x^2 \)). This gives us \( x^2 \).
2. **Multiply**: Multiply \( D(x) \) by \( x^2 \):
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