Abstract
This paper is dedicated to deriving some new formulas of the two classes of polynomials, namely k-Fibonacci and k-Lucas polynomials. New connection formulas between these two classes are developed. We show that the connection coefficients are expressed explicitly in terms of hypergeometric functions of the type F-2(1)( z), for certain z. Some linearization formulas of the two classes of polynomials are also given. New convolution identities involving the derivatives of the two classes of k-Fibonacci and k-Lucas polynomials are derived. As an important application of employing the two classes of polynomials, reduction formulas of some odd radicals are established.