Question

divide. if there is a remainder, include it as a simplified fraction. \\((16k^{3} + 48k^{2} + 32) \div 8k^{2}\\)

Explanation:

Step1: Split the polynomial division

$\frac{16k^3 + 48k^2 + 32}{8k^2} = \frac{16k^3}{8k^2} + \frac{48k^2}{8k^2} + \frac{32}{8k^2}$

Step2: Simplify each term

$\frac{16k^3}{8k^2}=2k$, $\frac{48k^2}{8k^2}=6$, $\frac{32}{8k^2}=\frac{4}{k^2}$

Step3: Combine simplified terms

$2k + 6 + \frac{4}{k^2}$

Answer:

$2k + 6 + \frac{4}{k^2}$