We are given three division problems. We need to divide the first polynomial by $m$, the second polynomial by $2mn$, and the third polynomial by $-y^2$.

1. Problem Description

We are given three division problems. We need to divide the first polynomial by $m$, the second polynomial by $2mn$, and the third polynomial by $-y^2$.

2. Solution Steps

Problem 2: $(-8m^3 + 12m^2 + 21m - 2) \div m$

We divide each term of the polynomial by $m$:

$\frac{-8m^3}{m} + \frac{12m^2}{m} + \frac{21m}{m} - \frac{2}{m}$

$= -8m^2 + 12m + 21 - \frac{2}{m}$

Problem 3: $(108m^3n - 122mn + 48m^2n) \div 2mn$

We divide each term of the polynomial by $2mn$:

$\frac{108m^3n}{2mn} - \frac{122mn}{2mn} + \frac{48m^2n}{2mn}$

$= 54m^2 - 61 + 24m$

Problem 4: $(y^5 - y^3z + y^2z^2) \div -y^2$

We divide each term of the polynomial by $-y^2$:

$\frac{y^5}{-y^2} - \frac{y^3z}{-y^2} + \frac{y^2z^2}{-y^2}$

$= -y^3 + yz - z^2$

3. Final Answer

Problem 2: $-8m^2 + 12m + 21 - \frac{2}{m}$

Problem 3: $54m^2 + 24m - 61$

Problem 4: $-y^3 + yz - z^2$