To find the quotient of the expression \( 24x^6 - 30x^4 \) divided by \( 6x^2 \), we can perform the division step by step.
Starting with the expression:
\[ \frac{24x^6 - 30x^4}{6x^2} \]
We can separate this fraction into two parts:
\[ \frac{24x^6}{6x^2} - \frac{30x^4}{6x^2} \]
Now we'll simplify each part individually.
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For the first term: \[ \frac{24x^6}{6x^2} = \frac{24}{6} \cdot \frac{x^6}{x^2} = 4x^{6-2} = 4x^4 \]
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For the second term: \[ \frac{30x^4}{6x^2} = \frac{30}{6} \cdot \frac{x^4}{x^2} = 5x^{4-2} = 5x^2 \]
Now combine the two results:
\[ 4x^4 - 5x^2 \]
Therefore, the quotient is:
\[ \boxed{4x^4 - 5x^2} \]
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