We show that abelian-by-polycyclic groups of homological type FP3 are virtually nilpotent-by-abellan. this generalizes earlier results of C. J. B. Brookes. We apply this to show that if G is the split extension of A by Q with A abelian, Q polycyclic and G of homological type FP3, then every quotient of G also has homological type FP3.o TEXTO COMPLETO DESTE ARTIGO, ESTARÁ DISPONÍVEL À PARTIR DE AGOSTO DE 2015.115609621UNICAMP, BrazilFAPEAM, Brazil