$\frac{6 x^{4} + 18 x^{3} - 3 x^{2}}{3 x^{2}}$ =

2 x^{2} + 6 x - 1

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2 x^{2} + 6 x + 1

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2 x^{2} - 6 x - 1

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x^{2} + 6 x - 1

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Solution

The correct option is A $2 x^{2} + 6 x - 1$
The given expression

$\frac{6 x^{4} + 18 x^{3} - 3 x^{2}}{3 x^{2}}$ can be written as,

$\frac{6 x^{4}}{3 x^{2}} + \frac{18 x^{3}}{3 x^{2}} - \frac{3 x^{2}}{3 x^{2}}$

$= \frac{2 \times 3 \times x \times x \times x \times x}{3 \times x \times x} + \frac{2 \times 3 \times 3 \times x \times x \times x}{3 \times x \times x} - \frac{3 \times x \times x}{3 \times x \times x}$

= $2 x^{2} + 6 x - 1$

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