We give an algorithm which can factor integers of the form
m
3 +
c
2
m
2 +
c
1
m +
c
0, where the
c
i are small integers. It is expected that the time required is
L
δ and the space required is
L
λ where
L = exp(Ö{log\text n\text log log n} )\text and d\text = r/Ö{6(r - 1)} \text, l = 2/Ö{6(r - 1)} ,L = \exp (\sqrt {\log {\text{ }}n{\text{ log log }}n} ){\text{ and }}\delta {\text{ = }}r/\sqrt {6(r - 1)} {\text{, }}\lambda = 2/\sqrt {6(r - 1)} ,
, where
r is the elimination exponent.