We report on a study of three-body charmless decays B+-->K(+)h(+)h(-) based on a 29.1 fb(-1) data sample collected with the Belle detector. With no assumptions on the intermediate mechanisms, the following three-body branching fractions have been measured for the first time: B(B+-->K(+)pi(-)pi(+)) = (55.6+/-5.8+/-7.7) x 10(-6) and B(B+-->K+K-K+) = (35.3+/-3.7+/-4.5) x 10(-6). We present the first observation of the decay B+-->f(0)(980)K+ with a branching fraction product of B(B+-->f(0)(980)K+) x B(f(0)(980)-->pi(+)pi(-)) = (9.6(-2.3-1.5-0.8)(+2.5+1.5+3.4)) x 10(-6). This is the first reported example of a B meson decay to a scalar pseudoscalar final state. We also report the first observation of B+-->K*(892)(0)pi(+) decay with a branching fraction of B(B+-->K*(892)(0)pi(+)) = (19.4(-3.9-2.1-6.8)(+4.2+2.1+3.5)) x 10(-6).
