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To factor the given polynomial \(9m^3 - 27m\) by its greatest common monomial factor:

1. **Find the greatest common factor (GCF)**:
   - The coefficients are 9 and 27, and the GCF of 9 and 27 is 9.
   - The variable \(m^3\) and \(m\) have a common factor of \(m\).
   
   Therefore, the GCF of the entire polynomial is \(9m\).

2. **Factor out the GCF**:
   - Divide each term by \(9m\).
   - \[
   9m^3 \div 9m = m^2, \quad -27m \div 9m = -3
   \]
   
   So, the factored form is:
   \[
   9m^3 - 27m = 9m(m^2 - 3)
   \]

Thus, the factored expression is:

\[
9m(m^2 - 3)
\]

Would you like further details on the factoring process or any related questions?

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Here are five related questions to deepen your understanding:
1. What is the general process of factoring polynomials by their greatest common factor?
2. How would you factor a polynomial if the GCF included more than one variable?
3. Can you factor the expression \(9m^3 - 27m\) further if possible?
4. How would you apply this technique to polynomials with four terms?
5. What other factoring techniques can be used if there is no common monomial factor?

**Tip**: Always check if the resulting expression can be factored further, such as factoring differences of squares or perfect square trinomials!

Factor the polynomial by its greatest common monomial factor: 9m^3 - 27m

Learn how to factor the polynomial 9m^3 - 27m by its greatest common factor. This problem demonstrates key algebraic techniques, including finding the GCF and factoring. Suitable for students in Grades 8-10.

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