Question

find the quotient.
\\(\frac{40s^6t^4 - 95s^5t^3 + 40s^4t^2 + 45s^2t}{5s^2t}\\)
enter the correct answer.

Explanation:

Step1: Divide each term by \(5s^2t\)

For the first term: \(\frac{40s^6t^4}{5s^2t} = \frac{40}{5} \cdot s^{6 - 2} \cdot t^{4 - 1} = 8s^4t^3\)
For the second term: \(\frac{-95s^5t^3}{5s^2t} = \frac{-95}{5} \cdot s^{5 - 2} \cdot t^{3 - 1} = -19s^3t^2\)
For the third term: \(\frac{40s^4t^2}{5s^2t} = \frac{40}{5} \cdot s^{4 - 2} \cdot t^{2 - 1} = 8s^2t\)
For the fourth term: \(\frac{45s^2t}{5s^2t} = \frac{45}{5} \cdot s^{2 - 2} \cdot t^{1 - 1} = 9\)

Step2: Combine the results

Combine the terms obtained from each division: \(8s^4t^3 - 19s^3t^2 + 8s^2t + 9\)

Answer:

\(8s^4t^3 - 19s^3t^2 + 8s^2t + 9\)