Using (771.6±10.6)×106 BB¯ meson pairs recorded by the Belle experiment at the KEKB e+e− collider, we report the branching fractions B(B¯0→D*+π−)=(2.62±0.02±0.09)×10−3 and B(B¯0→D*+K−)=(2.22±0.06±0.08)×10−4; the quoted uncertainties are statistical and systematic, respectively. A measurement of the ratio of these branching fractions is also presented, RK/π=B(B¯→D*+K−)/B(B¯→D*+π−)=(8.41±0.24±0.13)×10−2, where systematic uncertainties due to the D*+ meson reconstruction cancel out. Furthermore, we report a new QCD factorization test based on the measured ratios for B¯→D*+h− and B¯→D*+ℓ−ν decays at squared momentum transfer values equivalent to the mass of the h=π or K hadron. The parameters |a1(h)| are measured to be |a1(π)|=0.884±0.004±0.003±0.016 and |a1(K)|=0.913±0.019±0.008±0.013, where the last uncertainties account for all external inputs. These values are approximately 15% lower than those expected from theoretical predictions. Subsequently, flavor SU(3) symmetry is tested by measuring the ratios for pions and kaons, |a1(K)|2/|a1(π)|2=1.066±0.042±0.018±0.023, as well as for different particle species. The ratio is consistent with unity and therefore no evidence for SU(3) symmetry breaking effects is found at the 5% precision level.