Final answer:
The greatest common factor of 6u2 and 9u2 is 3u2, obtained by factoring out the common coefficient 3 and including the lowest common power of the variable, which is u2.
Step-by-step explanation:
To find the greatest common factor (GCF) of 6u2 and 9u2, you need to find the largest number that divides into both 6 and 9, and then include the common variables to the lowest power.
The GCF of 6 and 9 is 3 because 3 is the highest number that can evenly divide into both 6 (6 ÷ 3 = 2) and 9 (9 ÷ 3 = 3).
Since both terms have u2, we include this in the GCF.
Therefore, the GCF for 6u2 and 9u2 is 3u2.
- Factor each coefficient: 6 = 2 × 3, 9 = 3 × 3
- Common factor for coefficients is 3
- Variable part is u2 since it is common to both terms
- Combine the common factors: GCF = 3u2.