Find a function $\delta$ such that $(3x^3+x) \delta(x)^2 \rightarrow \infty$ and $(9x^3+x) \cdot \delta(x)^3 \rightarrow 0$

Let $f(x) := 3x^3+x$ and $g(x) := 9x^3+x$. Find a function $\delta$ such that $f(x) \cdot \delta(x)^2 \rightarrow \infty$ and $g(x) \cdot \delta(x)^3 \rightarrow 0$ for $x \rightarrow \infty$.

I can see that the condition $g(x) \cdot \delta(x) \rightarrow 0$ requires $\delta = \mathcal{o}(x^{-1/3})$, but I can not see how to connect this with the other condition, $f(x) \cdot \delta(x)^2 \rightarrow \infty$. Could you please help me?