52. \( \operatorname{Let}\left(x^{3}+p x^{2}+2 x-5\right)^{19}\left(x^{2}+q x-41\right)^{8}\left(x^{4}-x^{3}+x-7\right)^{6}=x^{97}+391 x^{96}+a_{955} x^{95}+a_{94} x^{94}+ \) \( \ldots a_{1} x+a_{0} \) be an identity, where \( p, q, a_{9} \ldots \) are antegers. Compute the smallest positive value of \( p \).

Question

\( \operatorname{Let}\left(x^{3}+p x^{2}+2 x-5\right)^{19}\left(x^{2}+q x-41\right)^{8}\left(x^{4}-x^{3}+x-7\right)^{6}=x^{97}+391 x^{96}+a_{955} x^{95}+a_{94} x^{94}+ \) \( \ldots a_{1} x+a_{0} \) be an identity, where \( p, q, a_{9} \ldots \) are antegers. Compute the smallest positive value of \( p \).