Question

Divide\[\sqrt{3} a^4 + 2\sqrt{3} a^3 + 3 a^2 - 6a\ \text{by}\ 3a\]

Answer 1

\[\frac{\sqrt{3} a^4 + 2\sqrt{3} a^3 + 3 a^2 - 6a}{3a}\]
\[ = \frac{\sqrt{3} a^4}{3a} + \frac{2\sqrt{3} a^3}{3a} + \frac{3 a^2}{3a} - \frac{6a}{3a}\]
\[ = \frac{1}{\sqrt{3}} a^{(4 - 1)} + \frac{2}{\sqrt{3}} a^{(3 - 1)} + a^{(2 - 1)} - 2\]
\[ = \frac{1}{\sqrt{3}} a^3 + \frac{2}{\sqrt{3}} a^2 + a - 2\]