How do we find the greatest common factor of a polynomial? Demonstrate the process with an example, showing your work. When finding the greatest common factor of a polynomial, can it ever be larger than the smallest coefficient? Can it ever be smaller than the smallest coefficient?

Question

anonymous · Answer

I am so stuck on this...so need help..if anyone can...sorry.

amistre64 · Answer

by intuition the smallest coeeficient is the bounds to the GCF.

How can you possibly have a number larger than the number you are factoring?

the largest facotr of any number is itself and 1, then they get smaller from there.

makes sense?

amistre64 · Answer

20 for example:

1,2,4,5 10, 20  these are the factors of 20.... they are limited to 1 thru 20

anonymous · Answer

Kind of....I guess...I am not having an easy time in this class and I am not sure why....but I never had to take this kind of stuff, and I get so confused

anonymous · Answer

huh, now that makes more sense to me...

amistre64 · Answer

if we have 2 number:  16 and 20  the biggest "common" number between them cannot be bigger than 16 right?  because what number greater than 16 is a factor of 16?  none.

amistre64 · Answer

20 factors to: 1,2,4,5,10,20 

16 factors to: 1,2,4,8,16

what is the largest number they have in common?

anonymous · Answer

ok...I really appreciate you helping me....this has gotten me all frustrated. I think I will be glad when this class is over. I will guess 4?

amistre64 · Answer

4 is absolutely correct.  it is the "greatest" "common" "factor"...thunder clap.......what!?! no thunder?....oh well, moving on :)

anonymous · Answer

lol....too funny...thanks for the laugh!

amistre64 · Answer

:)  keep practicing, youll get it ;)

anonymous · Answer

I completely understand what you are saying here, however how am I supposed to make an example for them?

anonymous · Answer

I sure hope so...this is kicking my butt!

amistre64 · Answer

id show them 16 and 20 and tell them that the number common between them is "smaller" than the smallest cooefficient, but can in no way be larger then the smallest coefficient...

make a polynomial like this perhaps:

20x +16

anonymous · Answer

ok...thanks so much:)

amistre64 · Answer

youre welcome :)