Find $f_{1}, f_{2}$ in $\mathbb{Z_{6}}[x]$ such that deg$(f_{1})$ = deg$(f_{2}) = 2$ and deg$(f_{1}+f_{2})=1$ 
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*Find $f_{1}, f_{2}$ in $\mathbb{Z_{6}}[x]$ such that deg$(f_{1})$ = deg$(f_{2}) = 2$ and deg$(f_{1}+f_{2})=1$

*Find $g_{1}, g_{2}$ in $\mathbb{Z_{6}}[x]$ such that deg$(g_{1})$ = deg$(g_{2}) = 1$ and deg$(g_{1}.g_{2})=1$


I have came up with this solution.
(1)  Let $f_{1}(x) = \bar{3}x^2+\bar{2}x+\bar{1}$ and $f_{2}(x) = \bar{3}x^2+x+\bar{2}$, which are of degree $2$. 
Then, $(f_{1}+f_{2}) = \bar{6}x^2 + \bar{3}x + \bar{3} = \bar{0}x^2 + \bar{3}x + 3$ is of degree $1$.
(2) Let $g_{1}(x) = 3+2x$ and $g_{2}(x) = 2+3x$, which are of degree $1$.
Then, $(g_{1}.g_{2}) = \bar{6} + \bar{13}x = \bar{0} + x$ is of degree $1$.
