Observation of the rare decay B+ -> K+ pi(0)pi(0) and measurement of the quasi-two-body contributions B+ -> K* (892)(+) pi(0), B+ -> f(0)(980)K+, and B+ -> chi K-c0(+)

We report an analysis of charmless hadronic decays of charged B mesons to the final state K+ pi(0)pi(0), using a data sample of (470.9 +/- 2.8) x 10(6) B (B) over bar events collected with the BABAR detector at the Y(4S) resonance. We observe an excess of signal events, with a significance above 10 standard deviations including systematic uncertainties, and measure the branching fraction and CP asymmetry to be B(B+ -> K+ pi(0)pi(0)) = (16.2 +/- 1.2 +/- 1.5) x 10(-6) and A(CP)(B+ -> K+ pi(0)pi(0)) = -0.06 +/- 0.06 +/- 0.04, where the uncertainties are statistical and systematic, respectively. Additionally, we study the contributions of the B+ -> K*(892)(+) pi(0), B+ -> f(0)(980)K+, and B+ -> chi K-c0(+) quasi-two-body decays. We report the world's best measurements of the branching fraction and CP asymmetry of the B+ -> K+ pi(0)pi(0) and B+ -> K+(892)(+) pi(0) channels.