How do I factorize $210a^6m^3-107a^4m^2l+18a^2l^2m-l^3$ into a term composed of multiplications of polynomials?

Question

I need to factorize $210a^6m^3-107a^4m^2l+18a^2l^2m-l^3$ into a term composed of multiplications of polynomials. WolframAlpha gave me the following answer $(6a^2m-l)(l-5a^2m)(l-7a^2m)$. Is there a method I could use to obtain this (or the factorization of any other polynomial? Thanks! :)

Answer 1

Hint: with $z = \cfrac{a^2m}{l}$ the expression writes as:

$$ l^3 \cdot \left(210 z^3 - 107 z^2+18 z -1\right) $$

Checking the cubic for rational roots finds the factorization:

$$ 210 z^3 - 107 z^2+18 z -1 = (7 z - 1) (6 z - 1) (5 z - 1) $$