Those polynomials that cannot be expressed as a product of non-trivial factors. For example, x²-2 is irreducible over the set of rational numbers, because there are no rational numbers A and B such that x²-2 = (x+A)(x+B).

Straight from Google:

http://mathworld.wolfram.com/IrreduciblePolynomial.html

http://www.math.niu.edu/~beachy/aaol/polynomials.html

http://en.wikipedia.org/wiki/Irreducible_polynomial

Straight from Google:

http://mathworld.wolfram.c

http://www.math.niu.edu/~b

http://en.wikipedia.org/wi