Question

Let g be the group of polynomials under addition with coefficients from z10. find the orders of f (x) 5 7x2 1 5x 1 4, g(x) 5 4x2 1 8x 1 6, and f (x) 1 g(x) 5 x2 1 3x.

Answer 1

f(x) = 7x^2 + 5x + 4, g(x) = 4x^2 + 8x + 6, and f(x) + g(x) = x^2 + 3x. If h(x) = \(undefined\) belongs to G, determine the order of h(x) given that gcd(a1, a2, ...,an) = 1; gcd(a1, a2, ...,an) = 2; gcd(a1, a2, ...,an) = 5; and gcd(a1, a2).