To find the greatest common factor (GCF) of the terms $x^2$, $x^3$, and $x^9$, we need to determine the highest power of $x$ that divides each term.

Step-by-Step Solution:

1. Identify the Powers of $x$:

   • For $x^2$, the exponent is 2.
   • For $x^3$, the exponent is 3.
   • For $x^9$, the exponent is 9.

2. Find the Lowest Power of $x$:

   • The exponents are 2, 3, and 9.
   • The smallest exponent is 2.

3. Determine the GCF:

   • The greatest common factor is $x^2$, since this is the highest power of $x$ that is a factor of all three terms.

Conclusion:

The greatest common factor (GCF) of $x^2$, $x^3$, and $x^9$ is: $\mathbf{x^2}$

Would you like more details or have any questions?

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Here are some related questions to further explore the topic:

1. How do you find the GCF for terms with coefficients and variables?
2. What is the difference between the least common multiple (LCM) and the greatest common factor (GCF)?
3. How do you factor a polynomial with multiple variables?
4. Can the GCF of two terms be larger than either of the terms?
5. How is finding the GCF useful in simplifying algebraic expressions?

Tip: When finding the GCF of terms with variables, always look for the smallest power of each variable that appears in all terms.