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

We report an analysis of charmless hadronic decays of charged B mesons to the final state K{sup +}{pi}{sup 0}{pi}{sup 0}, using a data sample of (470.9{+-}2.8)x10{sup 6} BB events collected with the BABAR detector at the {Upsilon}(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{sup +}{yields}K{sup +}{pi}{sup 0}{pi}{sup 0})=(16.2{+-}1.2{+-}1.5)x10{sup -6} and A{sub CP}(B{sup +}{yields}K{sup +}{pi}{sup 0}{pi}{sup 0})=-0.06{+-}0.06{+-}0.04, where the uncertainties are statistical and systematic, respectively. Additionally, we study the contributions of the B{sup +}{yields}K{sup *}(892){sup +}{pi}{sup 0}, B{sup +}{yields}f{sub 0}(980)K{sup +}, and B{sup +}{yields}{chi}{sub c0}K{sup +} quasi-two-body decays. We report the world's best measurements of the branching fraction and CP asymmetry of the B{sup +}{yields}K{sup +}{pi}{sup 0}{pi}{sup 0} and B{sup +}{yields}K{sup *}(892){sup +}{pi}{sup 0} channels.