Your Rational Mind's Optimum Age

Algebra Level pending

Let \(f(x)=Ax^3+Wx^2-x-H\) where \(A\) is your Age, \(W\) is your Weight, and \(H\) is your Height--all integers. There exists a healthy (W)eight that makes you feel taller while maintaining your mind's rational nature. Or, find \(W\) such that \(f(x)\) has a rational factor, and then completely factor \(f(x)\). Determine at what (A)ge your mind operates at peak rationality, or when \(f(x)\) has three rational factors.

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