Consider $x^{3}+8y^{3}+6xy-1$ as a polynomial over variable $x$.
$$x^{3}+6yx+8y^{3}-1$$
Find one factor of the form $x^{k}+m$, where $x^{k}$ divides the monomial with the highest power $x^{3}$ and $m$ divides the constant factor $8y^{3}-1$. One such factor is $x+2y-1$. Factor the polynomial by dividing it by this factor.
