To determine the greatest common factor (GCF) of the expressions [tex]\( 9x^2 \)[/tex] and [tex]\( 6x \)[/tex], we can follow these steps:
1. Factor each term:
- For [tex]\( 9x^2 \)[/tex]:
[tex]\[
9x^2 = 3^2 \cdot x^2
\][/tex]
- For [tex]\( 6x \)[/tex]:
[tex]\[
6x = 2 \cdot 3 \cdot x
\][/tex]
2. Identify the common factors:
- Both [tex]\( 9x^2 \)[/tex] and [tex]\( 6x \)[/tex] have the common factor [tex]\( 3 \)[/tex] and [tex]\( x \)[/tex].
3. Combine the common factors:
- Since both terms share the factor [tex]\( 3 \)[/tex] and [tex]\( x \)[/tex], their greatest common factor is the product of these common factors:
[tex]\[
3 \cdot x = 3x
\][/tex]
Therefore, the greatest common factor of [tex]\( 9x^2 \)[/tex] and [tex]\( 6x \)[/tex] is [tex]\( 3x \)[/tex].
So, the correct answer is:
(A) [tex]\( 3x \)[/tex]
