Find a factorable cubic polynomial with given conditions

Question

I want to write a factorable cubic polynomial in the form $Ax^3+Bx^2+Cx+D$ where $-D = 42C$. $A, B, C,$ and $D$ should be nonzero integers. Is this possible?

Answer 1

The polynomial $(x-2)(x+3)(x+7)$ works. We have $C=1$ and $D=-42$.

Added: OP asked in a comment whether one could make the roots positive. The answer is yes, the condition $-D=42C$ is not very constraining.

One simple example is $(x-126)^3$. Or else, for example, let us decide to look for a polynomial with roots $r,2r,3r$. Then $-D=42C$ becomes $6r^3=(42)(11r^2)$, giving $r=77$, and polynomial $(x-77)(x-154)(x-231)$.