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Let's break down how to find the **Greatest Common Factor (GCF)** for the terms in the list:

\[
-15x^3 \quad \text{and} \quad 6x^4
\]

### Step 1: Find the GCF of the numerical coefficients:
- The numbers are \(-15\) and \(6\). 
- The factors of \(15\) are: \(1, 3, 5, 15\).
- The factors of \(6\) are: \(1, 2, 3, 6\).
- The greatest common factor between \(-15\) and \(6\) is **3**.

### Step 2: Find the GCF of the variable part:
- For the variable \(x^3\) and \(x^4\), the GCF is the lowest power of \(x\), which is \(x^3\).

### Step 3: Combine the results:
- The GCF of the two terms is the product of the GCF of the numerical part and the variable part:  
  \[
  \text{GCF} = 3x^3
  \]

Thus, the **GCF** of \(-15x^3\) and \(6x^4\) is **3x³**.

Would you like further details on how the factors are derived, or do you have any questions?

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Here are 5 related questions for deeper understanding:
1. How do you find the GCF for a larger list of terms with multiple variables?
2. Can you explain why the GCF of variables is based on the lowest power?
3. How do you factor out the GCF from a polynomial expression?
4. What is the difference between GCF and LCM (Least Common Multiple)?
5. How does the sign of a term affect the GCF calculation?

**Tip**: When dealing with variables in GCF problems, always take the smallest exponent of each variable across all terms.

Learn how to find the GCF of two algebraic terms, -15x^3 and 6x^4. This problem involves finding the GCF of both the numerical coefficients and the variables with exponents. Suitable for students in Grades 9-10.

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