  The masses, atmospheric makeups, spin-orbit alignments, and system
architectures of extrasolar planets can be best studied when the planets orbit
bright stars. We report the discovery of three bodies orbiting HD 106315, a
bright (V = 8.97 mag) F5 dwarf targeted by our K2 survey for transiting
exoplanets. Two small, transiting planets have radii of 2.23 (+0.30/-0.25)
R_Earth and 3.95 (+0.42/-0.39) R_Earth and orbital periods of 9.55 d and 21.06
d, respectively. A radial velocity (RV) trend of 0.3 +/- 0.1 m/s/d indicates
the likely presence of a third body orbiting HD 106315 with period >160 d and
mass >45 M_Earth. Transits of this object would have depths of >0.1% and are
definitively ruled out. Though the star has v sin i = 13.2 km/s, it exhibits
short-timescale RV variability of just 6.4 m/s, and so is a good target for RV
measurements of the mass and density of the inner two planets and the outer
object's orbit and mass. Furthermore, the combination of RV noise and moderate
v sin i makes HD 106315 a valuable laboratory for studying the spin-orbit
alignment of small planets through the Rossiter-McLaughlin effect. Space-based
atmospheric characterization of the two transiting planets via transit and
eclipse spectroscopy should also be feasible. This discovery demonstrates again
the power of K2 to find compelling exoplanets worthy of future study.
