1. Factor the polynomial 12 x6 -25x4+30x3+20 in Z[x] or prove it cannot be done. 2. Expand (x-2)2(x-4)(x-6) in Z8[x] and findall the roots in Z8 of the result. Solution 2. Expand (x-2)2(x-4)(x-6) in Z8[x] and findall the roots in Z8 of the result. the roots are x = 2, 4 ,6 (x-2)2(x-4)(x-6) = (x2- 4x +4)(x2 -10x +24) = x4 - 10x3+24x2 -4x3 + 40x2 - 96x +4x2 - 40x +96 = x4 - 14x3 + 68x2 -136x +96.