  Let $R$ be a commutative ring with an identity different from zero and $n$ be
a positive integer. Anderson and Badawi, in their paper on $n$-absorbing
ideals, define a proper ideal $I$ of a commutative ring $R$ to be an
$n$-absorbing ideal of $R$, if whenever $x_1 \cdots x_{n+1} \in I$ for $x_1,
\ldots, x_{n+1} \in R$, then there are $n$ of the $x_i$'s whose product is in
$I$ and conjecture that $\omega_{R[X]}(I[X])=\omega_R(I)$ for any ideal $I$ of
an arbitrary ring $R$, where $\omega_R(I)= \min \{n\colon\text{$I$ is an
$n$-absorbing ideal of $R$}\}$. In the present paper, we use content formula
techniques to prove that their conjecture is true, if one of the following
conditions hold: The ring $R$ is a Pr\"ufer domain. The ring $R$ is a Gaussian
ring such that its additive group is torsion-free. The additive group of the
ring $R$ is torsion-free and $I$ is a radical ideal of $R$.
