  In this talk we discuss the next-to-leading-order electroweak (EW)
corrections to W-boson + jet hadroproduction [1] and compare the full result to
a simple approximation assuming factorization of EW and QCD corrections for the
charged-current Drell-Yan process. The W-boson resonance is treated
consistently using the complex-mass scheme, and all off-shell effects are taken
into account. The corresponding next-to-leading-order QCD corrections have also
been recalculated. All the results are implemented in a flexible Monte Carlo
code. Selected numerical results for this Standard Model benchmark process are
presented for the LHC. The comparison of our result to an approximation based
on the EW corrections to W-boson production without additional jets is a step
towards a better understanding of the interplay between QCD and EW effects for
W-boson production in general.
