How can I show that these polynomails are irreducible over rationals.
f(x) = x^4+x-1
h(x) = 1+x+x^2/2+x^3/6+x^4/24
j(x) = x^4-4x-1
I would assume you're expected to use the Rational Roots Theorem.
Given a polynomial , if , then is a factor of
How can I show that these polynomials are irreducible over rationals?
All the polynomials have a leading coefficient of 1.
. . So the only possible rational roots are factors of the constant term.
For (1), the only choices are: . Try them in
For (2), the only choices are: .
For (3), the only choices are: .
For (4), the only choices are: .