To simplify the expression \(12x^3 + 18x^2 - 30x\), we can factor out the greatest common factor (GCF) from all the terms.

### Step 1: Find the GCF
The GCF of 12, 18, and 30 is 6, and the GCF of \(x^3\), \(x^2\), and \(x\) is \(x\). Therefore, the overall GCF is \(6x\).

### Step 2: Factor out the GCF
Now, we factor out \(6x\) from each term:
\[
12x^3 + 18x^2 - 30x = 6x(2x^2 + 3x - 5)
\]

So, the factored form of the expression is:
\[
6x(2x^2 + 3x - 5)
\]

Let me know if you'd like to go further with solving or expanding this!

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Here are 5 related questions for you to consider:
1. How do you factor trinomials like \(2x^2 + 3x - 5\)?
2. What is the process for factoring higher-degree polynomials?
3. Can the quadratic \(2x^2 + 3x - 5\) be solved for its roots?
4. How would you use the factored form of a polynomial to graph its function?
5. What are common factoring mistakes to watch out for in algebra?

**Tip:** Always start by factoring out the greatest common factor (GCF) before attempting more complex factoring.

Learn how to factor the polynomial 12x^3 + 18x^2 - 30x by finding the greatest common factor (GCF). This step-by-step solution covers key algebraic concepts like factoring and polynomials. Suitable for students in Grades 8-10.

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