Cardinality of polynomials

Question

Lets say the set A consists of all the polynomials. And C denote the cardinal of real numbers. 1.) is the card (A) less than or equal to c? 2.) is the card of range of any nonconstant function from A = C? 3.) the range of any nonconstant function which can be expressed as a difference of two functions from A has card = C?

Answer 1

Hint:

1. A countably infinite union of sets of cardinality $C$ also has cardinality $C$
2. The set $\mathbb R^n$ has cardinality $C$, and so does any set with a bijecion to $\mathbb R^n$.
3. The set $A$ can be written as a countably infinite union of sets which, using point 2., can be shown to be of cardinality $C$.