Show tht if x is an integer, then gcd(x+1, x2-x+1) divides 3.

Which polynomial is the greatest common divisor of X5 + 2Xª – X – 2 and X4 +2X³ + X + 2 in Q[X]? Select one: O The polynomial X+ 2. O The polynomial 2X+1. O The polynomial X5 + 2. O None of the indicated polynomials. O The polynomial X? + 2.

(Please explain every step) Multiplication in GF(22) is polynomial multiplication reduced using the irreducible polynomial (x2 + x + 1) . Complete the multiplication table for GF(22). Do the multiplication as polynomials, reduce the answer mod (x2 + x + 1), write the result as a 2-bit pattern, then enter it in the table as hex. The row headed by 0 and the column headed by 0 are easy, as are the row headed by 1 and the column headed by 1. That leaves four entries. 2*2 : 2*3 : 3*2 : 3*3 :     * 0 1 2 3 0         1         2         3           Consider the set {1, 2, 3} and the operation * as shown in your table. (Notice that 0 has been removed from the set.) Show that the Group Axioms are followed:   Closed:     Associative     Identity:     Inverse:     Commutative:     Is this a multiplicative Abelian group? Now consider the distributive property: a*(b+c) = a*b + a*c   Using your tables, demonstrate that this holds for…

Find integers x and y so that gcd(2021, 271) = 2021x + 271y. Find integers m and n so that gcd (2021, 271) = 2021m+271n, m # x and n #y.

Calculate (-1+√3)120 using DeMoivre's formula. (show your work)

What values of x make 3(x – 5)(x – 12)(x + 5) = 0? If there is more than one answer, enter your answer as a comma-separated list. x = Preview Submit