Question

divide
\\(\frac{8z^4 - 32z^3}{4z^2}\\)
simplify your answer as much as possible.

Explanation:

Step1: Split the fraction

We can split the numerator into two separate fractions over the same denominator. So, \(\frac{8z^4 - 32z^3}{4z^2}=\frac{8z^4}{4z^2}-\frac{32z^3}{4z^2}\)

Step2: Simplify each fraction

For the first fraction \(\frac{8z^4}{4z^2}\), divide the coefficients and subtract the exponents of \(z\). The coefficient \(8\div4 = 2\), and for \(z\), \(z^{4 - 2}=z^2\), so this simplifies to \(2z^2\).
For the second fraction \(\frac{32z^3}{4z^2}\), divide the coefficients \(32\div4 = 8\), and for \(z\), \(z^{3 - 2}=z\), so this simplifies to \(8z\).
Putting it back together, we have \(2z^2-8z\)

Answer:

\(2z^{2} - 8z\)