  We exactly analyze, on the mean-field level, the low-momentum properties of a
single impurity atom loaded in the dilute one-dimensional Bose gas with two-
and three-body short-range interactions. Particularly the Bose polaron binding
energy and the quasiparticle residue are calculated for the considered system
in the broad region of parameters change. We also explore the generic
mean-field formula for the polaron effective mass which was shown to depend on
the density profile of bath particles with a motionless impurity immersed.
