How to factor out 6w3-14w2

Question

how do you factor out the greatest common monomial factor for 6w3-14w2

Answer 1

Factor 6w³-14w²

 

You need to do a "prime factorization" of the two terms in the expression; that is, factor each term down to prime numbers:

 

6w³ = 2*3*w*w*w

 

14w² = 2*7*w*w

 

The common factors between the two terms are 2*w*w = 2w².  So that's what you factor out.  If you take 2w² out of each term, you're left with:

 

6w3  -->  2*3*w*w*w = 3w
14w2 --> 2*7*w*w = 7

 

So the factored expression is:

 

2w²(3w-7)

 

To verify your answer, multiply out (distribute) the 2w² across the terms in the parentheses:

 

2w²(3w-7) = 2w²*3w - 2w²*7 = 6w³-14w²   CHECK!