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The image you provided shows a problem involving factoring polynomials using the greatest common factor (GCF). Let’s work through the problem step by step.

### Problem b:
The polynomial given is:

\[ 6x^4 - 9x^3 + 15x^2 - 12mx \]

#### Step 1: Identify the GCF
- **Coefficients**: The coefficients are 6, -9, 15, and -12. The GCF of these numbers is 3.
- **Variables**: The variables are \(x^4\), \(x^3\), \(x^2\), and \(x\). The smallest power of \(x\) in all the terms is \(x\). Therefore, the GCF for the variables is \(x\).

So, the GCF of the entire polynomial is \(3x\).

#### Step 2: Factor out the GCF
Now, factor \(3x\) out of each term in the polynomial:

\[
6x^4 - 9x^3 + 15x^2 - 12mx = 3x(2x^3 - 3x^2 + 5x - 4m)
\]

### Final Factored Form:
\[ 6x^4 - 9x^3 + 15x^2 - 12mx = 3x(2x^3 - 3x^2 + 5x - 4m) \]

This is the factored form of the polynomial using the greatest common factor.

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Do you want more details on any part of the solution? Here are some additional related questions to consider:

1. How do you determine the greatest common factor (GCF) of a set of terms?
2. What is the next step after factoring out the GCF in a polynomial?
3. How can you verify that the factoring was done correctly?
4. What if the polynomial was missing one term, how would that affect factoring?
5. How does factoring using the GCF differ from factoring by grouping?

**Tip:** When factoring polynomials, always start by identifying the GCF, as this simplifies the expression and makes it easier to factor further if needed.

Usando el mínimo común divisor, factoriza los siguientes polinomios: 6x^4 - 9x^3 + 15x^2 - 12mx

Learn how to factorize the polynomial 6x^4 - 9x^3 + 15x^2 - 12mx by using the Greatest Common Factor (GCF). This problem demonstrates key algebraic techniques suitable for students in Grades 8-10.

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