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p^{2}-9qp-22q^{2}
Consider p^{2}-9pq-22q^{2} as a polynomial over variable p.
\left(p-11q\right)\left(p+2q\right)
Find one factor of the form p^{k}+m, where p^{k} divides the monomial with the highest power p^{2} and m divides the constant factor -22q^{2}. One such factor is p-11q. Factor the polynomial by dividing it by this factor.