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\left(7p-4a\right)\left(p+8a\right)
Consider 7p^{2}+52ap-32a^{2} as a polynomial over variable p. Find one factor of the form kp^{m}+n, where kp^{m} divides the monomial with the highest power 7p^{2} and n divides the constant factor -32a^{2}. One such factor is 7p-4a. Factor the polynomial by dividing it by this factor.