Factor out GCF 18x to the 3 power +12x to the second power - 30x

Let's factor the greatest common factor (GCF) from the expression:

\[
18x^3 + 12x^2 - 30x
\]

1. Identify the GCF of the coefficients (18, 12, -30), which is 6.
2. All terms contain at least one factor of \(x\), so the GCF also includes \(x\).

Thus, the GCF is \(6x\).

Now, factor out \(6x\) from each term:

\[
18x^3 + 12x^2 - 30x = 6x(3x^2 + 2x - 5)
\]

The expression factored with the GCF is:

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

Would you like any more details or further explanation?

Here are five related questions:
1. How do you factor a trinomial like \(3x^2 + 2x - 5\)?
2. What is the greatest common factor (GCF) of multiple terms?
3. How do you determine the GCF of polynomial expressions?
4. Can a GCF include variables as well as numbers?
5. How do you factor quadratic expressions after factoring out the GCF?

**Tip:** Always check each term of the expression to ensure all common factors are included when factoring out the GCF.

Learn how to factor out the greatest common factor (GCF) from the polynomial expression 18x^3 + 12x^2 - 30x. This step-by-step guide covers key algebraic concepts, including factoring polynomials and finding the GCF. Ideal for students in Grades 8-10.

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