This content has been marked as final.
Show 1 reply

GCF and LCM of polynomials
TKHunny Mar 28, 2001 12:00 AM (in response to trae_leedisabled)y^{3}4y; y^{4}8y
As with every other GCF/LCM problem, your best approach MUST include a complete factorization.
y^{3}4y = y�(y^{2}4) = y�(y+2)�(y2)
y^{4}8y = y�(y^{3}8) = y�(y2)�(y^{2}+2y+4)
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)�(y2)
Then add whatever it does not have, that the other does.
y^{skip this one}�(y2)^{skip this one}�(y^{2}+2y+4)^{use this one}
y�(y+2)�(y2)�(y^{2}+2y+4)
Gives the LCM
GCF is the collection of factors that are common to all elements.
y�(y+2)�(y2)
y�(y2)�(y^{2}+2y+4)
Both have a 'y'
Both have a 'y2'
That's it.
y�(y2) is the GCF