  We present spectroscopic chemical abundances of red giant branch (RGB) stars
in Andromeda (M31), using medium resolution ($R\sim6000$) spectra obtained via
the Spectroscopic and Photometric Landscape of Andromeda's Stellar Halo
(SPLASH) survey. In addition to individual chemical abundances, we coadd low
signal-to-noise ratio (S/N) spectra of stars to obtain a high enough to measure
average [Fe/H] and [$\alpha$/Fe] abundances. We obtain individual and coadded
measurements for [Fe/H] and [$\alpha$/Fe] for M31 halo stars, covering a range
of 9--180 kpc in projected radius from the center of M31. With these
measurements, we greatly increase the number of outer halo ($R_{\mathrm{proj}}
> 50$ kpc) M31 stars with spectroscopic [Fe/H] and [$\alpha$/Fe], adding
abundance measurements for 45 individual stars and 33 coadds from a pool of an
additional 174 stars. We measure the spectroscopic metallicity ([Fe/H])
gradient, finding a negative radial gradient of $-0.0050\pm0.0003$ for all
stars in the halo, consistent with gradient measurements obtained using
photometric metallicities. Using the first measurements of [$\alpha$/Fe] for
M31 halo stars covering a large range of projected radii, we find a positive
gradient ($+0.0026\pm0.0004$) in [$\alpha$/Fe] as a function of projected
radius. We also explore the distribution in [Fe/H]--[$\alpha$/Fe] space as a
function of projected radius for both individual and coadded measurements in
the smooth halo, and compare these measurements to those stars potentially
associated with substructure. These spectroscopic abundance distributions
highlight the substantial evidence that M31 has had an appreciably different
formation and merger history compared to our own Galaxy.
