Write a polynomial that fits the following description: The polynomial has four terms and can be factored using a greatest common factor that has both a coefficient and a variable

A polynomial that fits the given description can be written as:

\[
6x^3 + 12x^2 + 18x + 24
\]

### Explanation:
- **Four terms**: The polynomial has four terms: \(6x^3\), \(12x^2\), \(18x\), and \(24\).
- **Greatest common factor (GCF)**: The greatest common factor of these terms is \(6x\), which is a product of a coefficient (6) and a variable (x).
  
Now, let's factor out the GCF:

\[
6x(x^2 + 2x + 3) + 6x(4) = 6x(x^2 + 2x + 4)
\]

This polynomial is factored with the GCF \(6x\).

Would you like more details or have any questions? Here are some related questions:

1. What is the greatest common factor, and how is it determined?
2. How do you factor out a greatest common factor (GCF) from a polynomial?
3. How do you check if a polynomial is factorable?
4. Can all polynomials be factored using a GCF?
5. What other types of factorization are common in algebra?

**Tip**: Always check for a GCF before attempting other factoring methods, as it simplifies the polynomial.

Learn how to write and factor a polynomial with four terms, focusing on identifying the greatest common factor (GCF) that includes both a coefficient and a variable. This problem introduces key algebraic concepts like GCF and polynomial factorization, suitable for students in Grades 8-10.

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