2. Let the polynomial $f(x)$ satisfy
$$
2 f(x+1)+3 f(x-1)=10 x^{2}+11 x+32 \text {. }
$$

Then $f(x)=$
2. $2 x^{2}+3 x+5$.

Notice that the degrees of $f(x+1)$ and $f(x-1)$ are the same, and the right side is quadratic, so let $f(x)=a x^{2}+b x+c$.
Substitute into the given equation and compare the coefficients on both sides to get
$$
a=2, b=3, c=5 \text {. }
$$

Therefore, $f(x)=2 x^{2}+3 x+5$.