Polynomial

I am with the first floor, but should the step be like this?

f(2x - 1) = Q(x) * 2x ----(1)

Let u = 2x - 1
x = (u+1)/2

Change all the x into u in (1)
f(u) = Q[(u+1)/2] * 2[(u+1)/2]
f(u) = Q[(u+1)/2] * (u+1)

[Change the variable u back to x]
f(x) = Q[(x+1)/2] * (x+1)

So, f(x) is divisible by (x + 1)

TamT:
f(2x - 1) is divisible by 2x. Not f(2x + 1) is divisible by 2x.

圖片參考：http://imgcld.yimg.com/8/n/HA08156933/o/701204220092713873397780.jpg

attempt only

f(2x - 1) = Q(x) * 2x

Let y = 2x - 1

f(y) = Q(2y - 1) * (y + 1)

So, f(x) is divisible by (y + 1)

2012-04-23 14:15:55 補充：
Sorry. f(x) is divisible by (x + 1)