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Algebra Level 5

\[\large P(x)=x^4+7x^3+2x-9\]

If \(a_1,a_2,a_3,a_4\) are roots of \(P(x)=0\) , find the sum of coefficients of a least degree monic polynomial whose roots are \(a_1a_2a_3,a_1a_2a_4,a_1a_3a_4,a_2a_3a_4\).

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