Factoring polynomials 6m⁴n² + 3m²n⁵

To factor the polynomial \(6m^4n^2 + 3m^2n^5\), follow these steps:

1. **Identify the Greatest Common Factor (GCF)**: Find the GCF of the coefficients and the variables.

    - For the coefficients 6 and 3, the GCF is 3.
    - For the variables \(m^4\) and \(m^2\), the GCF is \(m^2\).
    - For the variables \(n^2\) and \(n^5\), the GCF is \(n^2\).

    Therefore, the GCF of the polynomial \(6m^4n^2 + 3m^2n^5\) is \(3m^2n^2\).

2. **Factor out the GCF**: Divide each term of the polynomial by the GCF and factor it out.

    \[
    6m^4n^2 + 3m^2n^5 = 3m^2n^2(2m^2 + n^3)
    \]

So, the factored form of the polynomial \(6m^4n^2 + 3m^2n^5\) is \(3m^2n^2(2m^2 + n^3)\).

Would you like more details or have any questions?

Here are some related questions to further your understanding:

1. What is the process to find the GCF of a polynomial?
2. How do you factor a polynomial with more than two terms?
3. Can all polynomials be factored?
4. What are some common factoring techniques used in algebra?
5. How do you verify if a factored polynomial is correct?
6. What is the difference between factoring and simplifying a polynomial?
7. How can factoring polynomials be applied in solving equations?
8. What is the role of the distributive property in factoring polynomials?

**Tip:** When factoring polynomials, always look for the GCF first. It simplifies the process and makes further factoring steps easier.

Learn how to factor the polynomial 6m⁴n² + 3m²n⁵ with a detailed step-by-step solution. This problem covers key algebraic concepts, including factoring polynomials and identifying the Greatest Common Factor (GCF). Suitable for students in Grades 9-12.

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