In this paper, we investigate the relationship between small functions and differential polynomials $g_f\left(z\right)=d_2{f}^{\text{'}\text{'}}+d_1{f}^{\text{'}}+d_{0}f$, where $d_0\left(z\right)$, $d_1\left(z\right)$, $d_2\left(z\right)$ are entire functions that are not all equal to zero with $\rho \left(d_j\right)<1$$(j=0,1...$