Certainly! Let's go through the process of factoring out common factors step by step.

### Example Expression: \(6x^2 - 15x\)

#### Step 1: Identify the Greatest Common Factor (GCF)
To factor out, we first need to identify the greatest common factor (GCF) of the terms in the expression.

- For \(6x^2\):
  - The coefficient is \(6\), which factors into \(2 \times 3\).
  - The variable part is \(x^2\).

- For \(-15x\):
  - The coefficient is \(-15\), which factors into \(-1 \times 3 \times 5\).
  - The variable part is \(x\).

The GCF is the largest expression that can divide both terms. For \(6x^2\) and \(-15x\), the GCF is \(3x\) because:
- \(3\) is the largest common factor of \(6\) and \(15\).
- \(x\) is the common factor in the variable part.

#### Step 2: Factor Out the GCF
Now, we'll factor out the GCF, \(3x\), from each term:

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

#### Step 3: Write the Factored Form
After factoring out the GCF, the expression can be written as:

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

So, the factored form of \(6x^2 - 15x\) is \(3x(2x - 5)\).

### Final Answer
The expression \(6x^2 - 15x\) factors out to:

\[
3x(2x - 5)
\]

Would you like more examples or have any other questions?

Here are 8 related questions to further explore factoring:

1. What is the GCF of \(8x^3 - 12x^2 + 4x\)?
2. How would you factor out \(4a^2b - 12ab + 8ab^2\)?
3. Can you factor \(10x^2y - 25xy\) by finding the GCF?
4. How does factoring out work when there are more than two terms?
5. What if there is no common factor between the terms? What should you do?
6. How can we factor out negative terms, like \(-9x^2 + 3x\)?
7. How would you factor out the expression \(15y^3 + 20y^2 - 25y\)?
8. Can you factor out an expression that contains multiple variables, like \(4xy^2 - 6x^2y\)?

**Tip:** Always start by identifying the GCF before attempting to factor any algebraic expression.

Learn how to factor out common factors from algebraic expressions with a step-by-step guide. This problem covers key algebraic concepts, including factoring, polynomials, and finding the greatest common factor (GCF). Suitable for students in Grades 7-9.

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