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Let's analyze the expression and complete the statement:

The given expression is:

\[
12x^3 + 8x \div 4x
\]

### Step 1: Simplify the division first
The division in the expression is \( 8x \div 4x \).

- Simplifying:
  \[
  \frac{8x}{4x} = 2
  \]

So the entire expression becomes:

\[
12x^3 + 2
\]

### Step 2: Identify the components
- **Divisor**: This is the number by which we divide. In the part \( 8x \div 4x \), the divisor is \( 4x \).
- **Quotient**: The result of the division is \( 2 \), so the quotient is \( 2 \).
- **Dividend**: The dividend is the number being divided, which in this case is \( 8x \).

### Final Answer:
- Divisor: \( 4x \)
- Quotient: \( 2 \)
- Dividend: \( 8x \)

Would you like further details or any clarifications?

### Related Questions:
1. How do you simplify expressions with both multiplication and division of variables?
2. Can you factor the expression \( 12x^3 + 2 \)?
3. What happens if \( x = 0 \) in this case?
4. How do you handle polynomial division in more complex cases?
5. What are the common properties of divisors, dividends, and quotients in algebra?

### Tip:
Always simplify division and multiplication first before adding or subtracting in expressions!

In the expression 12x^3 + 8x ÷ 4x, the divisor is _______, the quotient is _______, and the dividend is ________.

Learn how to simplify the expression 12x^3 + 8x ÷ 4x step-by-step, identify the divisor, quotient, and dividend, and understand how to handle variables in algebraic division. Suitable for students in Grades 8-10.

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