To find the Greatest Common Monomial Factor (GCMF) of the given terms [tex]\(3x^2\)[/tex] and [tex]\(9y\)[/tex], we follow these steps:
1. Identify the coefficients and variables of each term:
- The term [tex]\(3x^2\)[/tex] has a coefficient of 3 and a variable part of [tex]\(x^2\)[/tex].
- The term [tex]\(9y\)[/tex] has a coefficient of 9 and a variable part of [tex]\(y\)[/tex].
2. Find the Greatest Common Divisor (GCD) of the coefficients:
- The coefficients are 3 and 9.
- The GCD of 3 and 9 is 3 because 3 is the largest number that divides both 3 and 9 exactly.
3. Find the common variables:
- Examine the variable parts of [tex]\(x^2\)[/tex] and [tex]\(y\)[/tex].
- There are no common variable parts because [tex]\(x^2\)[/tex] involves [tex]\(x\)[/tex] and [tex]\(y\)[/tex] involves [tex]\(y\)[/tex].
4. Combine the GCD of the coefficients with the common variables:
- Since there are no common variables, we only use the GCD of the coefficients.
Thus, the Greatest Common Monomial Factor (GCMF) of [tex]\(3x^2\)[/tex] and [tex]\(9y\)[/tex] is:
[tex]\[
3
\][/tex]
