The expression given is:

\[
6c^2 + 4c
\]

To fully factorize this, we can follow these steps:

1. **Find the greatest common factor (GCF)** of the terms \(6c^2\) and \(4c\).
   - The GCF of the coefficients \(6\) and \(4\) is \(2\).
   - The GCF of the variable part \(c^2\) and \(c\) is \(c\).

Thus, the GCF of the entire expression is \(2c\).

2. **Factor out the GCF**:

\[
6c^2 + 4c = 2c(3c + 2)
\]

Therefore, the fully factorized form is:

\[
2c(3c + 2)
\]

Would you like further details on any step?

Here are some related questions to explore:
1. How do you find the greatest common factor in polynomials?
2. What are the steps to factor quadratic expressions?
3. How do you solve factored equations?
4. Can you explain how factoring is used in solving equations?
5. How can factoring help in simplifying algebraic expressions?

**Tip:** Always check if the factored terms can be simplified further or factored again, especially in more complex polynomials.

Learn how to fully factorize the algebraic expression 6c^2 + 4c using the greatest common factor (GCF) method. This detailed guide walks through factoring polynomials by identifying the GCF and simplifying the expression. Suitable for students in Grades 6-8.

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