\(f\left(x\right)=ax^4+bx^3+cx^2+dx+e\)
\(f\left(-x\right)=ax^4-bx^3+cx^2-dx+e\)
\(\Rightarrow ax^4+bx^3+cx^2+dx+e=ax^4-bx^3+cx^2-dx+e\)
\(\Rightarrow2bx^3+2dx=0\) \(\forall x\Rightarrow\left\{{}\begin{matrix}2b=0\\2d=0\end{matrix}\right.\) \(\Rightarrow b=d=0\)
\(\Rightarrow f\left(x\right)=ax^4+cx^2+e\)
\(f\left(0\right)=e\Rightarrow e=2013\Rightarrow f\left(x\right)=ax^4+cx^2+2013\)
\(\left\{{}\begin{matrix}f\left(1\right)=a+c+2013=2035\\f\left(2\right)=16a+4c+2013=2221\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a=10\\c=12\end{matrix}\right.\)
\(\Rightarrow f\left(x\right)=10x^4+12x^2+2013\) \(\Rightarrow f\left(3\right)=2931\)
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