Measurements of branching fraction, polarization, and charge asymmetry of B±→ρ±f0 and a search for B±→ρ±f0(980)

We measure the branching fraction (B), polarization (f(L)), and CP asymmetry (A(CP)) of B-+/-->rho(+/-)rho(0) decays and search for the decay B-+/-->rho(+/-)f(0)(980) based on a data sample of 231.8x10(6) Upsilon(4S)-> B (B) over bar decays collected with the BABAR detector at the SLAC PEP-II asymmetric-energy B factory. In B-+/-->rho(+/-)rho(0) decays we measure B=(16.8 +/- 2.2 +/- 2.3)x10(-6), f(L)=0.905 +/- 0.042(-0.027)(+0.023), and A(CP)=-0.12 +/- 0.13 +/- 0.10, and find an upper limit on the branching fraction of B-+/-->rho(+/-)f(0)(980)(->pi(+)pi(-)) decays of 1.9x10(-6) at 90% confidence level.