Question

Is a^2 - 39 prime...

a. Over the set of polynomials with rational coefficients?
b. over the set of polynomials with real coefficients?
c. Explain your answers to Parts a and b

Answer 1

1) a) yes

b) no

c) a² - 39

(a)² - (sqrt(39))²

(a - sqrt(39))(a + sqrt(39))

This quadratic can be split into real factors, but not rational

sqrt(39) is a real number, but not rational since 39 is not a perfect square