A set S is constructed as follows. To begin, S={0,10}. Repeatedly, as long as possible, if x is an integer root of some polynomial anxn+an−1xn−1+...+a1x+a0, for some n≥1, all of whose coefficients ai are elements of S, and where an≠0, then x is put into S. When no more elements can be added to S, how many elements does S have?
This is another AMC question... and the problem is, I don't quite understand it. So when S={0,10}, what does the polynomial look like? Is it 0x2+10x because there are two numbers in the set? But then how would I account for a0? I'm really confused, and any help would really be appreciated!
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