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The problem in the image asks to use long division to divide the polynomial \( 24x^4 - 24x^3 - 18x^2 \) by \( 4x^3 + 2x^2 \) and write the answer in standard form.

### Step-by-step Solution:

We will use polynomial long division.

1. **Divide the first terms**:
   \[
   \frac{24x^4}{4x^3} = 6x
   \]
   So, the first term in the quotient is \( 6x \).

2. **Multiply** \( 6x \) by the divisor \( 4x^3 + 2x^2 \):
   \[
   6x \times (4x^3 + 2x^2) = 24x^4 + 12x^3
   \]

3. **Subtract**:
   \[
   (24x^4 - 24x^3 - 18x^2) - (24x^4 + 12x^3) = -36x^3 - 18x^2
   \]

4. **Divide the first terms**:
   \[
   \frac{-36x^3}{4x^3} = -9
   \]
   So, the next term in the quotient is \( -9 \).

5. **Multiply** \( -9 \) by the divisor \( 4x^3 + 2x^2 \):
   \[
   -9 \times (4x^3 + 2x^2) = -36x^3 - 18x^2
   \]

6. **Subtract**:
   \[
   (-36x^3 - 18x^2) - (-36x^3 - 18x^2) = 0
   \]

Thus, the quotient is:
\[
6x - 9
\]

### Final Answer:
\[
\boxed{6x - 9}
\]

Would you like more details on any part of this process?

### Related Questions:
1. How can we apply synthetic division to polynomials?
2. What is the remainder theorem for polynomial division?
3. How is dividing polynomials similar to dividing numbers?
4. Can we divide polynomials with higher degrees using the same method?
5. What are some common errors to avoid when performing polynomial long division?

### Tip:
When performing polynomial long division, ensure that the degrees of the terms are in descending order, and don't forget to subtract carefully!

Use long division to divide the polynomial 24x^4 - 24x^3 - 18x^2 by 4x^3 + 2x^2. Write your answer in standard form.

Learn how to use polynomial long division to divide 24x^4 - 24x^3 - 18x^2 by 4x^3 + 2x^2. This problem involves key algebraic concepts and is suitable for students in Grades 9-12.

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