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579 Views 1 Reply Latest reply: Mar 28, 2001 12:00 AM by TKHunny
60 posts since
Feb 8, 2001
Currently Being Moderated

GCF and LCM of polynomials

how do i find the GCF and LCM of these polynomials?

y^3-4y; y^4-8y
• 2,520 posts since
Sep 25, 2009
Currently Being Moderated
Mar 28, 2001 12:00 AM (in response to trae_lee-disabled)
GCF and LCM of polynomials
y3-4y; y4-8y

As with every other GCF/LCM problem, your best approach MUST include a complete factorization.

y3-4y = y�(y2-4) = y�(y+2)�(y-2)

y4-8y = y�(y3-8) = y�(y-2)�(y2+2y+4)

The LCM Zone

The LCM is the collection of factors that JUST contains each factor of each element. No need to count a factor from one element if it is already included in a previous element.

Just copy the first one:

y�(y+2)�(y-2)

Then add whatever it does not have, that the other does.

yskip this one�(y-2)skip this one�(y2+2y+4)use this one

y�(y+2)�(y-2)�(y2+2y+4)

Gives the LCM

The GCF Zone

GCF is the collection of factors that are common to all elements.

y�(y+2)�(y-2)
y�(y-2)�(y2+2y+4)

Both have a 'y'
Both have a 'y-2'

That's it.

y�(y-2) is the GCF

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