To divide the polynomial \( 18x^2 + 9x + 3 \) by \( -3x \), we can divide each term of the polynomial by \( -3x \).
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Divide \( 18x^2 \) by \( -3x \): \[ \frac{18x^2}{-3x} = -6x \]
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Divide \( 9x \) by \( -3x \): \[ \frac{9x}{-3x} = -3 \]
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Divide \( 3 \) by \( -3x \): \[ \frac{3}{-3x} = -\frac{1}{x} \]
Now, we can combine all these results: \[ -6x - 3 - \frac{1}{x} \]
So, the correct answer is A. -6x - 3 - 1/x.