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Is there a way to store the numerical values from a manipulate function in the form of a table? For example, if the function is

f[x_] := x^2 - 2x

Can one store all the values for each value of x in (0,1) from Manipulate[] other than taking a snapshot?

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I'm not sure what exactly you want to store. – Kuba Aug 15 '13 at 22:03
He wants to Append every value of the given mononomials / after decomposition of the function / to a table. – Sektor Aug 15 '13 at 22:09
If you can explain more. Do you mean you can to change x using a slider and have all the function values stored in a list for each x value changed. Then you want to click on a button to see the collected list? – Nasser Aug 15 '13 at 22:15
@Nasser He wants to decompose the polynomial and for every value of x, linked to the slider, to store the corresponding value of every mononomial in a table. – Sektor Aug 15 '13 at 22:31

There are infinite numbers between 0 and 1. Perhaps you want to memoize a finite subset of them.

Move the slider produced by the following code.

Manipulate[f[x] = x^2-2x, {x, 0, 1, .01}]

After that, run ?? f and you will get the values that were "stored".

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Clear[f]; f[x_] := f[x] = x^2 - 2 x
Manipulate[f[s], {s, 0, 1}]
Dynamic@Thread[{(Most@DownValues@f)[[All, 1, 
     1]] , (Most@DownValues@f)[[All, 2]]}]
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