Eisenstein's criterion
with integer coefficients is irreducible over the rationals if a prime number p exists such that:
(i) p divides each ai for i ≠ n;
(ii) p does not divide an;
(iii) p2 does not divide a0.
For example, xn − 2 is irreducible for all values of n. The criterion can also be usefully applied to cyclotomic polynomials. It cannot immediately be applied to x2 + x + 1, but if we set x = u + 1, then we obtain u2 + 3u + 3; this second polynomial is irreducible by the criterion (with p = 3) and, as it is irreducible, so is x2 + x + 1.
- two-sample tests
- two-sided test
- two-tailed test
- Tychonoff space
- Tychonoff's theorem
- Type I error
- Type II error
- typical sequence
- UFD
- UKMT
- ultrametric
- unary operation
- unbiased estimator
- unbounded
- unconditional statement
- uncountable
- undecidable
- underdetermined
- uniform
- uniform convergence
- uniform distribution
- uniform gravitational force
- uniformization theorem
- uniformly continuous
- uniform space