Answer:
5w³
Explanation:
To solve this, we can list the factors of each number and see which are common
25w⁵: separate this into 25 and w⁵ as one is a variable and one is not, so this will enable easier factorization. It is perfectly fine to separate these as these are multiplied by each other. For example, 5 is a factor of 25 but not of w⁵, but we can still factor 5 from 25w⁵ to get 5 (5w⁵)
factors of 25:
1, 5, 25
factors of w⁵:
1, w, w², w³, w⁴, w⁵
We know the factors of w⁵ because anything multiplied by 1 is equal to itself, w * w⁴ = w⁵, and w²*w³ = w⁵ due to exponent rules
Next,
factors of 5:
1, 5
factors of w⁴:
1, w, w², w³, w⁴
Finally,
factors of 15:
1, 3, 5, 15
factors of w³:
1, w, w², w³
For the constants, the greatest common factor is 5, and for the variables, the greatest common factor is w³
Because each value has both a constant and variable, we can use these two numbers to factor this out as
5w³(5w²+w + 3)