Subject - Theory of Computing ALEX is the set of valid algebraic expressions recursively defined by: Rule 1: All polynomials are in ALEX Rule 2: If f(x) and g(x) are in ALEX, then so are: i. (f(x)) ii. -(f(x)) iii. f(x) + g(x) iv. f(x) - g(x) v. f(x)g(x) vi. f(x)/g(x) vii. f(x)g(x) viii. f(g(x)) Assuming that the rules seen in class recursively defining polynomials can be used here to prove x+2 and 3x are polynomials, show that (x + 2)3x is in ALEX.

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