Factor the polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be​ factored, state this.

6 x plus 126x+12

To factor the polynomial \( 6x + 12 \) using the greatest common factor (GCF), follow these steps:

1. **Identify the GCF of the terms**: The two terms in the polynomial are \( 6x \) and \( 12 \).
   - The GCF of \( 6x \) and \( 12 \) is \( 6 \), because 6 is the largest number that divides both 6 and 12.

2. **Factor out the GCF**: 
   - When you factor out \( 6 \) from each term, you get:
     \[
     6x + 12 = 6(x + 2)
     \]

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

Would you like more details on this process or have any questions?

Here are some related questions you might find interesting:
1. How do you determine the GCF of polynomials with more than two terms?
2. What is the process for factoring polynomials with higher degrees?
3. Can a polynomial have more than one valid GCF?
4. What do you do if the polynomial includes variables with exponents?
5. How does factoring help in solving polynomial equations?

**Tip**: Always double-check your factored form by distributing the GCF back through the factored expression to ensure you obtain the original polynomial.

Learn how to factor the polynomial 6x + 12 using the greatest common factor (GCF). This problem covers key algebraic concepts related to polynomials and factoring. Suitable for students in Grades 7-9.

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