The LCM of f(x) = 20(x - 1)^3 (x + 2)^2, g(x) = 250(x - 1)^2 (x + 2) is _______... i'm not sure how to do this at all...

Answer 1

It is rather unusal to ask for the least common multiple of functions. It is not clear how "least" is defined

In this case I'd guess the LCM is
500(x-1)^3 *(x+2)^2
If you divide that by either of your two functions, you get a product of monomials and integers, with a lowest integer coefficient.

500(x-1)^3 *(x+2)^2/f(x) = 25
500(x-1)^3 *(x+2)^2/g(x) = 2(x-1)(x+2)