To factor the expression \(14x^2 + 21\) by the greatest common monomial factor (GCMF), follow these steps:

1. **Identify the Greatest Common Factor (GCF):**
   - The coefficients are 14 and 21. The GCF of 14 and 21 is 7.
   - The variable term in the first term is \(x^2\), but there is no variable in the second term, so the GCF will only include the numerical factor 7.

2. **Factor out the GCF:**
   - Divide each term by the GCF (7) and factor it out.
   \[
   14x^2 + 21 = 7(2x^2 + 3)
   \]

So, the factored form of \(14x^2 + 21\) is \(7(2x^2 + 3)\).

Would you like more details or have any questions about this? Here are some related questions you might find helpful:

1. How do you determine the GCF of more complex polynomials?
2. Can you explain the factoring process for trinomials?
3. What is the next step after factoring out the GCF if there's still a factorable polynomial inside?
4. How does factoring relate to solving quadratic equations?
5. Can every polynomial be factored by GCMF?

**Tip:** Always start by finding the GCF of all terms in the polynomial before trying other factoring techniques.

Learn how to factor the polynomial 14x^2 + 21 using the Greatest Common Monomial Factor (GCMF) method. Follow a step-by-step explanation to simplify and solve this problem. Suitable for students in Grades 7-9 studying algebra and polynomial factorization.

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