Irreducible Polynomial/Examples/x^2 + 1 in Complex Numbers
Jump to navigation
Jump to search
Examples of Irreducible Polynomials
Consider the polynomial:
- $\map P x = x^2 + 1$
over the ring of polynomials $\C \sqbrk X$ over the complex numbers.
Then $\map P x$ is not irreducible, as:
- $x^2 + 1 \equiv \paren {x + i} \paren {x - i}$
Sources
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $6$: Polynomials and Euclidean Rings: $\S 29$. Irreducible elements: Example $58$