Irreducible Polynomial/Examples/x^2 - 2 in Rationals

Examples of Irreducible Polynomials

Consider the polynomial:

$\map P x = x^2 - 2$

over the ring of polynomials $\Q \sqbrk X$ over the rational numbers.

Then $\map P x$ is irreducible.

Sources

• 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $6$: Polynomials and Euclidean Rings: $\S 29$. Irreducible elements: Example $58$