I have no clue how to do this:

A real number is said to be algebraic if it is a root of a polynomial equation

AnX^n + ..... A1X + A0 = 0

with integer coefficients. Note that algebraic numbers inclde the rationals and all roots of rationals (such as sqrt(2), cubert(5), ect.) If a number is not algebraic it is called transcendental.

A) show that the set of polynomials with integer coefficients is countable.

B) Show that the set of algebraic numbers is countable.

c) are thermore algebraic numbers or transcendental numbers?