Factor out the greatest common monomial factor: 2w^2+4w

Question

Factor out the greatest common monomial factor!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

Hello, thank you for taking the time to post your question!

The greatest common monomial factor (GCMF) means that you want to find the largest number that divides into both terms of the expression.

In this case that would be 2w, making the factored expression

2w(w + 2)

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Obviously this isn't me presenting this, but this is a very clear and concise video on how to do this:

http://www.virtualnerd.com/pre-algebra/factors-fractions-exponents/prime-factorization-greatest-common-factor/greatest-common-factor/greatest-common-factor-monomials

 

To put it here though:

You have the following:

2w² and 4w

You want to factor these out to their smallest prime factors

For 2w²:

First the 2, which factors out to 1 * 2.

Then factor the w², which factors out into w * w.

So the factors for 2w² are: 1 * 2 * w * w.  Don't worry about the 1, so you have 2 * w * w

 

Now for 4w:

First the 4 factors into 2 * 2.

Then the w factors into w.

So the factors of 4w are 2 * 2 * w.

Now look at what factors they have in common:

2 * w * w

2 * 2 * w

They both have a 2, so you make a note of the 2 (in the video she suggests circling it, I would personally write a 2, and mark through both 2s above so you know that you've already taken those out).

They also both have a w, so you do the same as with the 2 for the w.

Using my way, you would have this:

2 * w * w

2 * 2 * w

2, w

Now that you have a list of all the common factors of the expressions you were given, to get the greatest common factor, you multiply what you have in your list, so in this case it would be 2 * w, or 2w.