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For every constant $d$, we design a subexponential time deterministicalgorithm that takes as input a multivariate polynomial $f$ given as a constantdepth algebraic circuit over the field of rational numbers, and outputs allirreducible factors of $f$ of degree at most $d$ together with their respectivemultiplicities. Moreover, if $f$ is a sparse polynomial, then the algorithmruns in quasipolynomial time.  Our results are based on a more fine-grained connection between polynomialidentity testing (PIT) and polynomial factorization in the context of constantdegree factors and rely on a clean connection between divisibility testing ofpolynomials and PIT due to Forbes and on subexponential time deterministic PITalgorithms for constant depth algebraic circuits from the recent work ofLimaye, Srinivasan and Tavenas.

Deterministic Algorithms for Low Degree Factors of Constant Depth Circuits