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# factor out the gcf: 12x^2y^3z^4-2x^3yz^2

how would you do this?

Write it out so you have lots of space.  This particular problem has two terms.  So, to find the GCF we need to find ALL the things that these terms have in common.  I always like to start with the coefficients, but it's really up to you if you start with the variables or the coefficients. For simplicities sake, let's multiply those together and write it out again.  Remember that if you have numbers in the same term, you can multiply them together and the expression remains the same.

From there, we want to find the greatest common factor between what is now two coefficients: one in each term.  In other words, you want to find the biggest number that goes evenly into both coefficients.  Once you find it, write it outside the parenthesis, and divide both terms by the number you pick.  Rewrite your equation again so that you now have the expression, but with the greatest common factor of the coefficient outside the parenthesis.

Now,, lets look at the x's.  For any variable, the one with the lowest power will be the greatest common factor.  In this case, that is x2.  So, we are going to put the x2 as part of the GCF, outside the parenthesis.  Now, lets write out what we have left in the main expression.  To figure this out, we need to divide both terms by x2

you should follow the same process for y and z.  In the end, you will have your GCF on the outside of parenthesis, and rest of the expression inside them.  To double check your work, look at the main expression and make sure that the two terms have nothing else in common.  If this is true, good job! if not, just keep on factoring, multiplying the factors you pull out with the GCF, and dividing the main expression by the same.

First I'd rewrite it.  :)  (I know, you have it written out already and had to type it in here somehow)

12x22y33z4 - 2x3yz2

So, you have two terms here and there's a GCF for the the two.  Start with the coefficients 12 and 2.  What's the greatest common factor for those?  For simple numbers like this, you did these when you were figuring out lowest common denominator previously.  LCD = GCF for all intents and purposes.  Write this down on the next line.

Next, look at the x variable in each term.  The one with the lowest power will be the GCF.  Put it next to your GCF for the coefficients.

Do the same thing for y and z.

Now you have your GCF, but you haven't factored it.

Divide each term by it and put the result in parenthesis next to the GCF.