Divide:

15a³b⁴ - 10a⁴b³ - 25a³b⁶ by -5a³b²

(15a³b⁴ - 10a⁴b³ - 25a³b⁶) ÷ (-5a³b²)

= (15a³b⁴ ÷ (- 5a³b²)) - (10a⁴b³ ÷ (- 5a³b²)) - (25a³b⁶ ÷ (- 5a³b²))

= $\Big($- $\dfrac{15}{5}$ a^(3-3)b^(4-2)$\Big)$ - $\Big($- $\dfrac{10}{5}$ a^(4-3)b^(3-2)$\Big)$ - $\Big($- $\dfrac{25}{5}$ a^(3-3)b^(6-2)$\Big)$

= - 3 a⁰b² + 2 a¹b¹ + 5 a⁰b⁴

= - 3b² + 2 ab + 5b⁴

Hence, (15a³b⁴ - 10a⁴b³ - 25a³b⁶) ÷ (- 5a³b²) = - 3b² + 2 ab + 5b⁴