eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2020-07-22 8 3 57 69 10.12691/tjant-8-3-2 TJANT2020832 article Aziz ATTA azizatta20@gmail.com 1 Atta Engineering Design Office (Study and Technical Assistance), El Jadida, Morocco Polynomials and matrices have played a very important role in the development of different branches of mathematics. Indeed, several mathematicians have introduced classical polynomials very useful for the scientific community such as the Lagrange¡¯s interpolation polynomials, the Chebyshev¡¯s polynomials and the Bernstein¡¯s polynomials [1,2]. Also, there is a strong link between polynomials and matrices through the notions of the determinant, the characteristic polynomial and the minimal polynomial. Similarly, we will introduce in this article two polynomials which we will call twin polynomials as well as a matrix called kernels matrix. Finally, we will present some applications such as the resolution of recurrent sequences with second member and the establishment of several sum formulas. http://pubs.sciepub.com/tjant/8/3/2/tjant-8-3-2.pdf factorial mean twin polynomials factorial means staircase kernels matrix kernels determinant