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Identify the greatest common factor of 25w⁵+5w⁴+15w³​

User Wouter Verlaek
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1 Answer

17 votes
17 votes

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)

User Xirema
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