Question

1. $(2x^{4}+5x^{2}-3x)\div6x^{3}$

Explanation:

Step1: Split the polynomial fraction

$\frac{2x^4 + 5x^2 - 3x}{6x^3} = \frac{2x^4}{6x^3} + \frac{5x^2}{6x^3} - \frac{3x}{6x^3}$

Step2: Simplify each term

$\frac{2x^4}{6x^3} = \frac{x}{3}$, $\frac{5x^2}{6x^3} = \frac{5}{6x}$, $\frac{3x}{6x^3} = \frac{1}{2x^2}$

Step3: Combine simplified terms

$\frac{x}{3} + \frac{5}{6x} - \frac{1}{2x^2}$

Answer:

$\frac{x}{3} + \frac{5}{6x} - \frac{1}{2x^2}$