Dalitz-plot analysis of the decays<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>B</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>∓</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>±</mml:mo></mml:msup></mml:math>

We report a Dalitz-plot analysis of the charmless hadronic decays of charged B mesons to the final state K(+/-)pi(-/+)pi(+/-). Using a sample of 226.0 +/- 2.5 million B (B) over bar pairs collected by the BABAR detector, we measure the magnitudes and phases of the intermediate resonant and nonresonant amplitudes for both charge-conjugate decays. We present measurements of the corresponding branching fractions and their charge asymmetries that supersede those of previous BABAR analyses. We find the charge asymmetries to be consistent with zero. RI Peters, Klaus/C-2728-2008; de Groot, Nicolo/A-2675-2009; Patrignani, Claudia/C-5223-2009; Lista, Luca/C-5719-2008; Bellini, Fabio/D-1055-2009; Roe, Natalie/A-8798-2012; Neri, Nicola/G-3991-2012; Monge, Maria Roberta/G-9127-2012