Question

(6x^2 + x + 3)x(5x^2 + 2) in Z_10 =

(a) x^3 + 2x + 6

(b) 5x^3 + 7x^2 + 2x + 6

(c) x^3 + 7x^2 + 2x + 6

(d) None of the mentioned

The question was asked by my college director while I was bunking the class.

I'm obligated to ask this question of Polynomial and Modular Arithmetic- IV in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

Answer 1

Correct option is (b) 5x^3 + 7x^2 + 2x + 6

Best explanation: (6x^2 + x + 3)x(5x^2 + 2) in Z_10 =  5x^3 + 7x^2 + 2x + 6. We can find this via basic polynomial arithmetic in Z_10.