To find the quotient of \( 24x^6 - 30x^4 \) divided by \( 6x^2 \), we can follow these steps:
- Factor out the common term from the numerator.
- Divide each term in the numerator by \( 6x^2 \).
Let's start with the expression:
\[ \frac{24x^6 - 30x^4}{6x^2} \]
Step 1: Factor out the common term from the numerator.
We can factor out \( 6x^4 \) from the numerator:
\[ 24x^6 - 30x^4 = 6x^4(4x^2 - 5) \]
Step 2: Substitute the factored form back into the quotient.
Now substitute the factored form into the division:
\[ \frac{6x^4(4x^2 - 5)}{6x^2} \]
Step 3: Simplify the expression.
We can now cancel \( 6 \) from the numerator and the denominator, and also \( x^2 \):
\[ \frac{x^4(4x^2 - 5)}{x^2} = x^{4-2}(4x^2 - 5) = x^2(4x^2 - 5) \]
Final Result:
The quotient is:
\[ x^2(4x^2 - 5) \]
This can also be expressed as:
\[ 4x^4 - 5x^2 \]
Either form is acceptable, but the expression \( x^2(4x^2 - 5) \) is a simpler factored form.