Murphy to determine the gcd of x^(2)+x^(6)-3x^(3)+3x^(2)+2x-5 3x^(6)+5

1.	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» 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.

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»

We first factorize the GIVEN polynomials x

−x−2,x

+x−6 and 3X

−13x+14 as shown below:

−x−2

−2x+x−2

=x(x−2)+1(x−2)

=(x−2)(x+1)

+x−6

+3x−2x−6

=x(x+3)−2(x+3)

=(x−2)(x+3)

−13x+14

=3x

−6x−7x+14

=3x(x−2)−7(x−2)

=(x−2)(3x−7)

The common FACTOR of x

−x−2,x

+x−6 and 3x

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