L = Z5[x]/(x^2+2x+4) is a field and the multiplicative group L* is generated as a cyclic group by s+3, where s is the congruence class of x modulo x^2+2x+4. Prove the following statements about the orders of elements in L*.
(a) s has order 12.
(b) s+1 has order 8.
(c) s+2 has order 12.
(d) 2s has order 6.
I thought this problem wouldn't be so bad but I am having difficulties. Any help would be appreciated!