Thus, the only non-constant irreducible polynomials over are linear polynomials.

As shown in the examples above, only linear polynomials are irreducible over the field of complex numbers (this is a consequence of the fundamental theorem of algebra).

Comparing this to the definition of O(1), above, we see that the sections of O(1) are in fact linear homogeneous polynomials, generated by the themselves.

The factors are either linear polynomials representing well isolated zeros or higher order polynomials representing clusters of zeros.

This recursion stops after a finite number of proper splits with all factors being nontrivial powers of linear polynomials.

The third necessary condition in Bunyakovsky's conjecture for a linear polynomial is equivalent to and being relatively prime.

For instance, given a linear polynomial on a vector space, one can determine its constant part by evaluating at 0.

Linear interpolation is a method of curve fitting using linear polynomials.

Vielhaber claims, for instance, that the linear polynomials in the key bits that are obtained during the attack will be unusually sparse.

Any (usual) integer z Z is an algebraic integer, as it is the zero of the linear monic polynomial: