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My question is: if G:= Group of polynomials under addition with elements from $\{0,1,2,3,4,5,6,7,8,9\}$ $f(x)=7x^2+5^x+4$ and $g(x)=4x^2+8^x+6$ ,$f(x)+g(x)=x^2+3x$ what is the order of $f(x)$,$g(x)$,$f(x)+g(x)$ i find that the answers are $10$,$5$ and $10$ . Am i correct?? (i noticed that zero polynomial is the identity here) then if $h(x)=a_nx^n+...+a_0$ belongs to $G$ what is the order of it? given that

$gcd(a_1,a_2,,,a_n)=1$,

$gcd(a_1,a_2,,,,a_n)=2$,

$gcd(a_1,a_2,,,a_n)=5$,

$gcd(a_1,a_2,,,a_n)=10$

Here i do not understand how to proceeded ?

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