we have the function
[tex]g(x)=-x(x^2+3)(x-2)^3(x+5)^2[/tex]
In this problem, we have that
the leading coefficient is negative (-1)
The degree of the function is 8 (even)
therefore
the end behavior of the function is
f(x)→−∞, as x→−∞
f(x)→−∞, as x→+∞
