\( (f \cdot g)(x)=-x^{4}-4 x^{3}+38 x^{2}+24 x-192 \) (Simplify your answer.)

To simplify the expression \( (f \cdot g)(x)=-x^{4}-4 x^{3}+38 x^{2}+24 x-192 \), we can factor it or analyze it further. Let's start by looking for possible rational roots using synthetic division or the Rational Root Theorem. Testing a few values, you might find that \( x=2 \) is a root. After synthetic division by \( x-2 \), you'll reduce the polynomial to a cubic. Continuing this process, you may discover more roots and ultimately express the polynomial in factored form, making it easier to analyze. Alternatively, plotting this polynomial or using technology can also reveal critical points and behavior, allowing you to better understand the function's characteristics.