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Using long division, the result of dividing \( 6x^3 + 13x^2 + 12x + 4 \) by \( 3x + 2 \) is:

\[
2x^2 + 3x + 2
\]

There is no remainder, meaning the division is exact.

Would you like further details on the steps of polynomial long division?

Here are five related questions:
1. How do you apply synthetic division instead of long division for similar problems?
2. What is the difference between polynomial long division and synthetic division?
3. Can long division be applied to non-polynomial expressions?
4. How do we handle polynomial division when the divisor is not a binomial?
5. What if there were a remainder? How would we represent it in the final answer?

**Tip**: When the remainder is zero in polynomial division, the divisor is a factor of the dividend.

Use the long division method to find the result when 6x^3 + 13x^2 + 12x + 4 is divided by 3x + 2.

Learn how to divide the polynomial 6x^3 + 13x^2 + 12x + 4 by 3x + 2 using the long division method. This step-by-step solution explains the key concepts of polynomial division, making it suitable for students in Grades 10-12.

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