Math Problem Statement

Factoring polynomials 6m⁴n² + 3m²n⁵

Solution

To factor the polynomial 6m4n2+3m2n56m^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 m4m^4 and m2m^2, the GCF is m2m^2.
    • For the variables n2n^2 and n5n^5, the GCF is n2n^2.

    Therefore, the GCF of the polynomial 6m4n2+3m2n56m^4n^2 + 3m^2n^5 is 3m2n23m^2n^2.

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

    6m4n2+3m2n5=3m2n2(2m2+n3)6m^4n^2 + 3m^2n^5 = 3m^2n^2(2m^2 + n^3)

So, the factored form of the polynomial 6m4n2+3m2n56m^4n^2 + 3m^2n^5 is 3m2n2(2m2+n3)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.

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Math Problem Analysis

Mathematical Concepts

Polynomials
Factoring
Greatest Common Factor (GCF)

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12