I was studying cubic factorisation and had just begun to get the hang of it. Cubic equations which are of the form $$ax^3+bx^2+cx+d:\frac{a}{b}=\frac{c}{d}$$ are naturally straightforward to solve, but I've been especially intrigued with those which cannot be factorised by the usual grouping method, such as $f(x)=6x^3+17x^2+14x+3$. I started using the Remainder and Factor Theorems to factorise these, but when I put this same equation into Google for factorisation, to check whether I understood my concept right, it provided the steps in the following manner.
This method seems relatively faster, but wherever I search, the only methods I find are directly or indirectly related to either the Remainder Theorem-based method to find roots where $f(x)=0$ holds true or the long cubic formula.
Does anyone here have any idea of the logic behind the first step used by Google's solution here, and does this method used work for all cubics or only those which satisfy a certain condition? Any additional information on this would be greatly appreciated. Thankyou!