The material of this publication can be regarded as the continuation of the author's previous publication (ISBN: 978-620-0-62498-7) with the same title. It can also be regarded as a supplement, containing additional tables, longer listings than the ones given before, and additional figures. In this second part the factorization of the compressed Chebyshev polynomials via cyclotomic pre-polynomials are mainly emphasized. It is shown that the factorization of the compressed Chebyshev polynomials of all kinds and the factorization of certain very simple polynomials are fully synchron with each other in the meaning that all factors of the formers are cyclotomic pre-polynomials, while the factors of the latters are the corresponding cyclotomic polynomials. Some of the tables summarize the most important general properties and identities (among them the factorizational formulas) with the four kinds of Chebyshev polynomials and their modified variants. These tables apply to arbitrary positive integer n in general. Another set of tables are listings for the values of n between 1 and 20. A long table contains the parallel listing of cyclotomic pre-polynomials and cyclotomic polynomials.