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**How do you know which factor to use???**

I know what factoring is. Basically, you take any given number or expression, and rewrite it as a product of its factors.

For instance in 3xy + 9y, every term is divisable by "3y", so we could rewrite it as 3y(x + 3).

But, consider: [tex]\displaystyle{28xy^2 - 14x}[/tex]

Every term there is divisible by "14x", so is there something at all wrong with: [tex]\displaystyle{14x(2y^2 - 1)}[/tex]???

That's how I would factor it, but the book instead choose to use "7x" as the factor, and uses [tex]\displaystyle{7x(4y^2 - 2)}[/tex] as the answer.

If given an exam, how do you know which factor they are going to claim is the "correct" one????

Thanks a lot.