Question

The sum of polynomials of degrees m and n has degree max[m,n].

(a) True

(b) False

(c) Can’t Say

(d) None of the mentioned

I got this question in a national level competition.

I need to ask this question from Polynomial and Modular Arithmetic- III topic in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

Answer 1

The correct option is (c) Can’t Say

Easiest explanation: True when m is not equal to n; in that case the highest degree coefficient is of degree max[m,n]. But false in general when m = n, because the highest-degree coefficients might cancel (be additive inverses).