To determine a common factor among the given terms, we need to look for the greatest common factor (GCF) across all terms listed.
The terms provided are:
- 6x²y
- 8x²
- 30y
- 40
- x⁴
- 3y⁴
- x²
- 4
- 3y⁵
Let’s break down each term into its prime factors:
- 6x²y = 2 × 3 × x² × y
- 8x² = 2³ × x²
- 30y = 2 × 3 × 5 × y
- 40 = 2⁵ × 5
- x⁴ = x⁴
- 3y⁴ = 3 × y⁴
- x² = x²
- 4 = 2²
- 3y⁵ = 3 × y⁵
Now, we identify the common terms between the factors of all the expressions. The common numerical factors are 2 (appearing in multiple terms, like 6, 8, 30, and 40) and 3 (appearing in terms 6, 30, and 3).
Looking at the variables, the least power of x across the terms is x² and for y, the least power is y in terms like 6x²y and 30y.
Therefore, the GCF is determined by taking the lowest powers of the common primes and variables present in each term.
Thus, a common factor that we can take out from all these terms is:
2y (since 2 is the lowest with at least one occurrence in factors that include y)
In conclusion, 2y is a common factor of the terms 6x²y, 8x², 30y, 40, x⁴, 3y⁴, x², 4, and 3y⁵.