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We measure the branching fraction (B), polarization (fL), and CP asymmetry (ACP) of B±→ρ±ρ0 decays and search for the decay B±→ρ±f0(980) based on a data sample of 231.8×106 Υ(4S)→B¯¯¯B decays collected with the BABAR detector at the SLAC PEP-II asymmetric-energy B factory. In B±→ρ±ρ0 decays we measure B=(16.8±2.2±2.3)×10−6, fL=0.905±0.042+0.023−0.027, and …