Which of these polynomials are irreducible in Qx a x4 x2

Which of these polynomials are irreducible in Q[x] ? (a) x^4 - x^2 + 1 (b) x^4 + x + 1 (c) x^5 + 4x^4 + 2x^3 + 3x^2 - x + 5 (d) x^5 + 5x^2 + 4x + 7

Solution

Polynomial a, b are irreducable because they cant be split into functions in given rational plane

c)can be written as(x+3.725)f(x) and (d) can be written as (x+1.715)g(x) in rational plane, when we plot a graph we can easily determine the roots for the given equation.