Let f(x),g(x)"\\in Q[x]"
Then there exists q(x) and r(x)"\\in Q[x]" such that f(x)=g(x)q(x)+r(x) where either r(x)=0 or deg(r)<deg(g). (Since Q is a field, division algorithm holds in Q[x])
When r"\\neq 0" , deg(r)<deg(g) "\\Rightarrow" 2"^ {deg(r)}" <2"^{deg(g)}" "\\Rightarrow d(r)<d(g)"
We also note d"(fg)=2^{deg(fg)}= 2^{deg(f)+deg(g)}=2^{deg(f)} 2^{deg(g)}=d(f)d(g)"
Hence d is an Euclidean evaluation.
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