If f(x)=x^3-2x^2-x+5, then the remainder of g(x)=f(f(x)) divided by (x-2) is

Answer 1

If you multiplied this all out it would be a nightmare - VERY easy to make a simple mistake which will goof up the answer. A much easier way is to use the remainder theorem which says that the remainder is g(2). Then you can use your calculator to do the rest.

f(2) = 3 and then, since we are doing f(f(2)), f(3) = 11

So the remainder is 11

Answer 2

f(2) = 8 - 8 - 2 + 5 = 3; f(f(2)) = f(3) = 27 - 18 - 3 + 5 = 11.