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The expression given is \( 12x + 6 \), and the task is to factor it completely.

### Solution:

1. First, identify the greatest common factor (GCF) of the terms \( 12x \) and \( 6 \).
   - The GCF of 12 and 6 is 6.

2. Factor out the GCF:
   \[
   12x + 6 = 6(2x + 1)
   \]

So, the factored form of \( 12x + 6 \) is \( 6(2x + 1) \).

### Verification (Check by multiplying):
To verify, multiply back:
\[
6(2x + 1) = 6 \cdot 2x + 6 \cdot 1 = 12x + 6
\]
This confirms that the factorization is correct.

Would you like any further details or clarification?

Here are five related questions:
1. How do you find the greatest common factor of two terms?
2. Can all binomials be factored using a GCF?
3. What are other factoring methods for expressions with more terms?
4. How would you factor an expression like \( 15x + 9 \)?
5. Why is checking your factorization by multiplying back important?

**Tip:** Always start by factoring out the GCF before applying other factoring techniques!

Factor 12x + 6 completely. Check by multiplying.

Learn how to factor the algebraic expression 12x + 6 by finding the greatest common factor. This step-by-step guide helps students understand key algebra concepts such as factoring and applying the distributive property. Suitable for students in Grades 6-8.

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