algorithmics mathematics

IT SHOULD BE SOMETHING LIKE THAT :::::::

1. Let F = Z/(7), E = F[x]. Determine the output of GCD(5x + 4x +3, x+6) for the following GCD algorithm. Use a table and write new values of variables and expressions explicitly in your solution. Algorithm GCD INPUT: a,b E E. OUTPUT: G E E, such that g is a gcd of a and b. if b=0 then return a; else return GCD(b, a MOD b); fi; end; Example 5.43. Let F =Z/(5), E = F[2]. We determine GCD (x2 + 2x +1, x2 + 4). GCD (x2 + 2x + 1,x2 + 4) Alg a b b=0 | a MODb GCDX(b, a MODb) return GCD 2? + 2x +1 22 +4 F 2x + 2 GCD2 (x2 + 4, 2x + 2) 2x + 2 GCD2 22 +4 2.0 + 2 F 0 GCD: (2.0 +2,0) 2.0 + 2 GCD3 2.0 +2 0 T 2.0 +2 return 2.c + 2