Final answer:
To divide the polynomial (-8v⁴z⁶+32v²z) by (4v³z²), divide each term of the numerator by the denominator, resulting in the simplified expression -2vz⁴ + 8/(vz).
Step-by-step explanation:
The division of the polynomial expression (-8v⁴z⁶+32v²z) by (4v³z²) is approached by dividing each term of the numerator separately by the denominator. Simplify the expression step by step:
- Divide the first term: (-8v⁴z⁶) ÷ (4v³z²) = -2vz⁴
- Divide the second term: (32v²z) ÷ (4v³z²) = 8v-1z-1 = 8/(vz)
Combining these results, the simplified expression is -2vz⁴ + 8/(vz).