How to prove that all polynomials with rational coefficients are countable sets?

This can be derived from the properties of countable sets
1. The set of rational numbers q is countable
2. The product of countable set is countable = > Q × Q ×. × Q countable = = > the polynomials with rational coefficients less than or equal to n terms are countable
3. Countable union of countable sets is countable = = > all rational coefficient polynomials are countable

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