Question

What is the quotient of \frac{24x^6-30x^4}{6x^2}

Answer 1

To find the quotient of the expression \(\frac{24x^6 - 30x^4}{6x^2}\), we'll divide each term in the numerator by the denominator separately.

1. Start by dividing the first term in the numerator:
\[
\frac{24x^6}{6x^2} = \frac{24}{6} \cdot \frac{x^6}{x^2} = 4x^{6-2} = 4x^4.
\]

2. Now, divide the second term in the numerator:
\[
\frac{30x^4}{6x^2} = \frac{30}{6} \cdot \frac{x^4}{x^2} = 5x^{4-2} = 5x^2.
\]

Now we can combine the results:
\[
\frac{24x^6 - 30x^4}{6x^2} = 4x^4 - 5x^2.
\]

Thus, the quotient is:
\[
\boxed{4x^4 - 5x^2}.
\]