Exercise
Suppose x 
C is a zero of
the nonzero polynomial f Q[X].
Then, by definition, x is algebraic. If x is nonzero,
then x-1 is also algebraic.
Of which polynomial is it a zero?
1/f(X)
f(X-1)
Xnf(X-1),
where n = deg(f).
No. In general, this is not even a polynomial.
No. In general, this is not even a polynomial.
Correct. After multiplying out, the result is indeed a polynomial.