Playing with Vieta

Algebra Level 5

x4+37x3+71x2+18x+3 \large x^4 + 37x^3 + 71x^2 + 18x + 3

If aa, bb, cc, and dd represent the roots of the polynomial above, find the sum of the coefficients of the monic polynomial whose roots are abcd \large\frac{abc}{d}, abdc\large \frac{abd}{c}, acdb\large\frac{acd}{b}, and bcda \large\frac{bcd}{a}.

Inspiration.

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