Authors’ summary: Generalizations of Binet’s theorem are used to produce generalized Pell sequences from two families of silver means. These Pell sequences are also generated from the family of Fibonacci polynomials. A family of Pell-Lucas sequences are also generated from the family of Lucas polynomials and from another generalization of Binet’s formula. A periodic set of cyclic constants are generated from the Lucas polynomials. These cyclic constants are related to the Gauss-Wantzel proof of the constructibility by compass and straightedge regular polygon.