Question

find the quotient.
\\(\frac{70n^4 - 74n^3 - 36n}{2n}\\)
enter the correct answer.

Explanation:

Step1: Divide each term by \(2n\)

We can split the fraction \(\frac{70n^4 - 74n^3 - 36n}{2n}\) into three separate fractions: \(\frac{70n^4}{2n}-\frac{74n^3}{2n}-\frac{36n}{2n}\)

Step2: Simplify each fraction

• For \(\frac{70n^4}{2n}\), divide the coefficients and subtract the exponents of \(n\): \(\frac{70}{2}n^{4 - 1}=35n^3\)
• For \(\frac{74n^3}{2n}\), divide the coefficients and subtract the exponents of \(n\): \(\frac{74}{2}n^{3 - 1}=37n^2\)
• For \(\frac{36n}{2n}\), divide the coefficients and subtract the exponents of \(n\) (note that \(n^1/n^1 = n^{0}=1\)): \(\frac{36}{2}\times1 = 18\)

Putting it all together, we get \(35n^3-37n^2 - 18\)

Answer:

\(35n^3 - 37n^2 - 18\)