Evidence for direct CP violation in B ±→ηh ± and observation of B0→ηK0

We report measurements of the branching fractions and CP asymmetries for B-+/- -> eta h(+/-) (h = K or pi) and the observation of the decay B-0 -> eta K-0 from the final data sample of 772 x 10(6) B (B) over bar pairs collected with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. The measured branching fractions are B(B-+/- -> eta K-+/-) = (2.12 +/- 0.23 +/- 0.11) x 10(-6), B(B-+/- -> eta pi(+/-)) = (4.07 +/- 0.26 +/- 0.21) x 10(-6), and B(B-0 -> eta K-0) = (1.27(-0.29)(+0.33) +/- 0.08) x 10(-6), where the last decay is observed for the first time with a significance of 5.4 standard deviations (sigma). We also find evidence for CP violation in the charged B modes, A(CP)(B-+/- -> eta K-+/-) = -0.38 +/- 0.11 +/- 0.01 and A(CP)(B-+/- -> eta pi(+/-)) = -0.19 +/- 0.06 +/- 0.01 with significances of 3.8 sigma and 3.0 sigma, respectively. For all measurements, the first and second uncertainties are statistical and systematic, respectively.