Consider $15x^{2}+22xy+8y^{2}$ as a polynomial over variable $x$.
$$15x^{2}+22yx+8y^{2}$$
Find one factor of the form $kx^{m}+n$, where $kx^{m}$ divides the monomial with the highest power $15x^{2}$ and $n$ divides the constant factor $8y^{2}$. One such factor is $3x+2y$. Factor the polynomial by dividing it by this factor.