  We analyse the broad-range shape of the monopole and quadrupole correlation
functions of the BOSS Data Release 12 (DR12) CMASS and LOWZ galaxy sample to
obtain constraints on the Hubble expansion rate $H(z)$, the angular-diameter
distance $D_A(z)$, the normalised growth rate $f(z)\sigma_8(z)$, and the
physical matter density $\Omega_mh^2$. We adopt wide and flat priors on all
model parameters in order to ensure the results are those of a `single-probe'
galaxy clustering analysis. We also marginalise over three nuisance terms that
account for potential observational systematics affecting the measured
monopole. However, such Monte Carlo Markov Chain analysis is computationally
expensive for advanced theoretical models, thus we develop a new methodology to
speed up our analysis. We obtain $\{D_A(z)r_{s,fid}/r_s$Mpc,
$H(z)r_s/r_{s,fid}$kms$^{-1}$Mpc$^{-1}$, $f(z)\sigma_8(z)$, $\Omega_m h^2\}$ =
$\{956\pm28$ , $75.0\pm4.0$ , $0.397 \pm 0.073$, $0.143\pm0.017\}$ at $z=0.32$
and $\{1421\pm23$, $96.7\pm2.7$ , $0.497 \pm 0.058$, $0.137\pm0.015\}$ at
$z=0.59$ where $r_s$ is the comoving sound horizon at the drag epoch and
$r_{s,fid}=147.66$Mpc for the fiducial cosmology in this study. In addition, we
divide the galaxy sample into four redshift bins to increase the sensitivity of
redshift evolution. However, we do not find improvements in terms of
constraining dark energy model parameters. Combining our measurements with
Planck data, we obtain $\Omega_m=0.306\pm0.009$,
$H_0=67.9\pm0.7$kms$^{-1}$Mpc$^{-1}$, and $\sigma_8=0.815\pm0.009$ assuming
$\Lambda$CDM; $\Omega_k=0.000\pm0.003$ assuming oCDM; $w=-1.01\pm0.06$ assuming
$w$CDM; and $w_0=-0.95\pm0.22$ and $w_a=-0.22\pm0.63$ assuming $w_0w_a$CDM. Our
results show no tension with the flat $\Lambda$CDM cosmological paradigm. This
paper is part of a set that analyses the final galaxy clustering dataset from
BOSS.
