https://file.aiquickdraw.com/mathbot/file/17241489074308dp21orn.jpg

The expression in the image is:

\[
15x^2 + 30x
\]

To solve this by factoring, follow these steps:

1. **Identify the greatest common factor (GCF):**
   - The GCF of \(15x^2\) and \(30x\) is \(15x\).

2. **Factor out the GCF:**
   - When you factor \(15x\) out of both terms, you get:
   \[
   15x(x + 2)
   \]

So, the factored form of the expression \(15x^2 + 30x\) is:

\[
15x(x + 2)
\]

Would you like more details, or do you have any questions about this process?

Here are some related questions to expand your understanding:

1. What would be the factored form if the expression was \(15x^2 + 45x\)?
2. How do you factor a quadratic expression that doesn't have a common factor?
3. What is the next step after factoring when solving a quadratic equation?
4. Can you factor the expression \(15x^2 + 30x + 45\)? If so, how?
5. What are the roots of the equation \(15x^2 + 30x = 0\)?

**Tip:** Always start by identifying the greatest common factor when factoring an expression, as it simplifies the process.

Learn how to solve mathematical problems using factoring terms with a detailed step-by-step solution. This problem covers key algebraic concepts, including factoring polynomials and quadratic equations. Suitable for students in Grades 9-12.

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