The expression \(6x^3 + 15x^2\) can be factored by finding the greatest common factor (GCF) of the two terms.

1. **Identify the GCF of the coefficients**: 
   - The GCF of \(6\) and \(15\) is \(3\).

2. **Identify the GCF of the variable parts**:
   - The GCF of \(x^3\) and \(x^2\) is \(x^2\).

3. **Factor out the GCF**:
   - The GCF of the expression is \(3x^2\).

So, the factored form is:

\[
6x^3 + 15x^2 = 3x^2(2x + 5)
\]

Would you like any further details or have any questions?

Here are 5 related questions for practice:
1. Factor \(8x^3 + 12x^2\).
2. Simplify the expression \(9x^4 + 15x^3\).
3. Factor \(10x^3 + 25x^2 + 15x\).
4. What is the GCF of \(14x^5\) and \(21x^3\)?
5. Factor \(18x^4 + 27x^3\).

**Tip:** Always look for the greatest common factor first when factoring expressions; it simplifies the expression and makes further factoring easier if needed.

Learn how to factor the polynomial 6x^3 + 15x^2 step-by-step. This problem involves finding the greatest common factor (GCF) of the coefficients and the variable parts. Suitable for students in Grades 7-9.

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