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Find the GCF of (6x, 9x^2)

Sagot :

pierceashmore12
The correct answer (the GCF) is 3x.
AL2006

Well, when we're asked for a GCF, it's usually for two numbers, not two
algebraic expressions.  But let's see what we can do with these anyway.

What are the factors of  6x ?
How about 1, 2, 3, x, 2x, 3x, and 6x ?
If you divide 6x by any thing on that list, you get something else
on the list, so it's actually a list of the factors of  6x .

And what are the factors of  9x² ?
How about 1, 3, 9, x, 3x, 9x, x², 3x², and 9x² ?
If you divide  9x²  by any thing on that list, you get something else
on the list, so it's actually a list of the factors of  9x² .

What are the 'common' factors ... the ones that are on both lists ?

1, 3, x, and 3x .

What's the biggest one ?

It could depend on what number 'x' is ... that's is why I have a personal
problem with 'the GCF' of algebraic expressions.  But as long as 'x' is
any substantial number, then the biggest factor on the 'common' list is 3x .


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