Question

Murphy to determine the gcd of x^(2)+x^(6)-3x^(3)+3x^(2)+2x-5 3x^(6)+5x^(4)-4x^(2)-9x+21 over GF13 using Euclidean d algorithm

Answer 1

Explanation:

We first factorize the given polynomials x

2

−x−2,x

2

+x−6 and 3x

2

−13x+14 as shown below:

x

2

−x−2

=x

2

−2x+x−2

=x(x−2)+1(x−2)

=(x−2)(x+1)

x

2

+x−6

=x

2

+3x−2x−6

=x(x+3)−2(x+3)

=(x−2)(x+3)

3x

2

−13x+14

=3x

2

−6x−7x+14

=3x(x−2)−7(x−2)

=(x−2)(3x−7)

The common factor of x

2

−x−2,x

2

+x−6 and 3x

2

−13x+14 is (x−2), therefore, the GCD is x−2.