Irreducible Polynomial/Examples/x^2 + 1 in Real Numbers

Examples of Irreducible Polynomials

Consider the polynomial:

$\map P x = x^2 + 1$

over the ring of polynomials $\R \sqbrk X$ over the complex numbers.

Then $\map P x$ is irreducible, as its factors:

$x^2 + 1 \equiv \paren {x + i} \paren {x - i}$

are complex.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): reducible polynomial
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): reducible polynomial