What must be added to `f(x)=4x^4+2x^3-2x^2+x-1` so that the resulting polynomial is divisible by `g(x)=x^2+2x-3.`

Explanation

To determine what must be added to the polynomial \( f(x) = 4x^4 + 2x^3 - 2x^2 + x - 1 \) so that it becomes divisible by \( g(x) = x^2 + 2x - 3 \), we will perform polynomial long division and find the remainder. The value that needs to be added will be the negative of this remainder.

### Step-by-Step Solution:

1. **Set Up the Division**: We want to divide \( f(x) \) by \( g(x) \). We write it as:
\[ f(x) = (x^2 + 2x - 3) \cdot Q(x) + R(x) \]
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