To find the quotient of the polynomial \(6t^3 - 6t^2 + 12t\) divided by \(22\), we can first express the polynomial and then divide each term by \(22\).
The polynomial is: \[ 6t^3 - 6t^2 + 12t \]
Now, we divide each term by \(22\):
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For the term \(6t^3\): \[ \frac{6t^3}{22} = \frac{3t^3}{11} \]
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For the term \(-6t^2\): \[ \frac{-6t^2}{22} = \frac{-3t^2}{11} \]
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For the term \(12t\): \[ \frac{12t}{22} = \frac{6t}{11} \]
Now, we can combine these results: \[ \frac{6t^3 - 6t^2 + 12t}{22} = \frac{3t^3}{11} - \frac{3t^2}{11} + \frac{6t}{11} \]
We can write the entire expression as a single fraction: \[ \frac{3t^3 - 3t^2 + 6t}{11} \]
Thus, the quotient of \(6t^3 - 6t^2 + 12t\) divided by \(22\) is: \[ \frac{3t^3 - 3t^2 + 6t}{11} \]