Thread: Back to the roots

Originally Posted by kenny1999

Hi everyone, although I am able to solve some very advanced maths, I think I still have lots of basic concepts that I am still not clear. It is the
first day I am here so I 'd like to take this chance to ask.

Back to the roots... what is L.C.M. and what is H.C.F.?

L.C.M. is "least common multiple"- the smallest quantity that is a multiple of both (or all) numbers or expressions. H.C.F. is highest common factor (I would say "gcd"-greatest common divisor). It is the largest number or expression that divides all given numbers or expressions.

and what is the H.C.F. of

16ab and 24a^2

16= 8*2 and 24= 8*3 so 8 is the largest number that will divide both 16 and 24. 16ab has one but not two factors of "a" and 23a^2 does not have a "b" so the H.C.F of 16ab and 24a^2 is 8a.
Although you didn't ask, the L.C.M. is 48a^2b.

another question is :

how many methods to divide a polynomials in x by another polynomials in x?
and what are the methods? I really forget these things

How "methods" are there to divide numbers? There really only one "method"- old fashioned "long division". So called "synthetic division" is just a version of that for very simple cases.

By the way, is there any websites that explain some general concepts like the above? Because I have become a mathematics teacher recently, I hope to review some resources to help me recall some simple concepts and learn the way to explain to my students

Thanks all

Originally Posted by kenny1999

what is L.C.M. and what is H.C.F.?

and what is the H.C.F. of 16ab and 24a^2

how many methods to divide a polynomials in x by another polynomials in x?
and what are the methods?

...is there any websites that explain some general concepts like the above?

There are loads of sites. Try searching for specific topics:

. . . . .Google results for "LCM GCF"

. . . . .Google results for "factoring polynomials"

. . . . .Google results for "dividing polynomials"

If you notice certain helpful sites showing up frequently, you might want to bookmark them for future reference. :wink: