2 The elements of a group \(G\) are polynomials of the form \(a + b x + c x ^ { 2 }\), where \(a , b , c \in \{ 0,1,2,3,4 \}\). The group operation is addition, where the coefficients are added modulo 5 .
- State the identity element.
- State the inverse of \(3 + 2 x + x ^ { 2 }\).
- State the order of \(G\).
The proper subgroup \(H\) contains \(2 + x\) and \(1 + x\).
- Find the order of \(H\), justifying your answer.