Irreducible polynomial

In mathematics, an irreducible polynomial is, roughly speaking, a non-constant polynomial that cannot be factored into the product of two non-constant polynomials. The property of irreducibility depends on the field or ring to which the coefficients are considered to belong. For example, the polynomial $x - 2$ is irreducible if the coefficients 1 and −2 are considered as integers, but it factors as $(x-\sqrt{2})(x+\sqrt {2})$ if the coefficients are considered as real numbers. One says that "the polynomial $x - 2$ is irreducible over the integers but not over the reals".

单词	Reducible polynomial
释义	Reducible polynomial 英语百科 Irreducible polynomial In mathematics, an irreducible polynomial is, roughly speaking, a non-constant polynomial that cannot be factored into the product of two non-constant polynomials. The property of irreducibility depends on the field or ring to which the coefficients are considered to belong. For example, the polynomial $x - 2$ is irreducible if the coefficients 1 and −2 are considered as integers, but it factors as $(x-\sqrt{2})(x+\sqrt {2})$ if the coefficients are considered as real numbers. One says that "the polynomial $x - 2$ is irreducible over the integers but not over the reals".
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Reducible polynomial

Irreducible polynomial