In base 2, these objects 
In base 2, these objects are designated primitive if they generate maximum period linear feedback shift registers. The Chebyshev ones are a special case of the Jacobi ones, as are the Legendre ones. A Taylor series of order n corresponds to one of these with degree n, and irreducible ones cannot be factored, though the fundamental theorem of algebra guarantees they have at least one complex root. For 10 points, identify these mathematical objects whose terms are all proportional to a power of a variable, examples of which include 3y and x squared plus 1.
In base 2, these objects are designated primitive if they generate maximum period linear feedback shift registers.
polynomials