What must be subtracted from `8x^4+14 x^3-2x^2+7x-8` so that the resulting polynomial is exactly divisible by `4x^2+3x-2.`

Explanation

To solve the problem of what must be subtracted from the polynomial \( 8x^4 + 14x^3 - 2x^2 + 7x - 8 \) so that the resulting polynomial is exactly divisible by \( 4x^2 + 3x - 2 \), we will perform polynomial long division and find the remainder. The remainder will be the polynomial that needs to be subtracted.

### Step-by-Step Solution:

1. **Set Up the Division**: We need to divide \( 8x^4 + 14x^3 - 2x^2 + 7x - 8 \) by \( 4x^2 + 3x - 2 \).

2. **First Division**:
- Divide the leading term of the dividend \( 8x^4 \) by the leading term of the divisor \( 4x^2 \):
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