Questions: Divide: (10 m^5 n^2-30 m n)/(5 m n) 5 m^4 n-25 2 m^4 n-30 m n 2 m^4 n-6 2 m^6 n^3-6 m^2 n^2

Solution Steps

To solve the given problem, we need to divide the polynomial \(10m^5n^2 - 30mn\) by \(5mn\). This involves dividing each term in the numerator by the denominator.

1. Divide the first term \(10m^5n^2\) by \(5mn\).
2. Divide the second term \(-30mn\) by \(5mn\).
3. Simplify the resulting terms.

We start with the polynomial expression \(10m^5n^2 - 30mn\) and the divisor \(5mn\).

We divide the polynomial by the divisor: \[ \frac{10m^5n^2 - 30mn}{5mn} \]

We simplify the division term by term:

1. For the first term: \[ \frac{10m^5n^2}{5mn} = 2m^4n \]
2. For the second term: \[ \frac{-30mn}{5mn} = -6 \]

Combining these results, we have: \[ 2m^4n - 6 \]

Final Answer