arens regularity of bilinear forms and unital banach module spaces

assume that $a$‎, ‎$b$ are banach algebras and that $m:atimes brightarrow b$‎, ‎$m^prime:atimes arightarrow b$ are bounded bilinear mappings‎. ‎we study the relationships between arens regularity of $m$‎, ‎$m^prime$ and the banach algebras $a$‎, ‎$b$‎. ‎for a banach $a‎$‎-bimodule $b$‎, ‎we show that $b$ factors with respect to $a$ if and only if $b^{**}$ is unital as an $a^{**}‎$‎-module‎. ‎let $z_{e^{primeprime}}(b^{**})=b^{**}$ where $e^{primeprime}$ is a mixed unit of $a^{**}$‎. ‎then $b^*$ factors on both sides with respect to $a$ if and only if $b^{**}$ has a unit as $a^{**}‎$‎-module‎.