The problem asks to divide the polynomial $47108m^3n - 122mn + 48mn^2$ by $2mn$.

1. Problem Description

The problem asks to divide the polynomial $47108m^3n - 122mn + 48mn^2$ by $2mn$.

2. Solution Steps

We need to divide each term of the polynomial by $2mn$.

First term: $\frac{47108m^3n}{2mn} = \frac{47108}{2} \cdot \frac{m^3}{m} \cdot \frac{n}{n} = 23554m^{3-1} \cdot 1 = 23554m^2$.

Second term: $\frac{-122mn}{2mn} = \frac{-122}{2} \cdot \frac{m}{m} \cdot \frac{n}{n} = -61 \cdot 1 \cdot 1 = -61$.

Third term: $\frac{48mn^2}{2mn} = \frac{48}{2} \cdot \frac{m}{m} \cdot \frac{n^2}{n} = 24 \cdot 1 \cdot n^{2-1} = 24n$.

Combining these terms, we get $23554m^2 - 61 + 24n$.

3. Final Answer

$23554m^2 - 61 + 24n$