Here is what the problem asks for:
Give an example of a polynomial function f of degree 5 such that the only real roots of f(x) are -2,1,6 and
f(2)=32. Show that your example works and leave f(x) in factored form.
Since f(x) is of degree 5 and f(x) has three real roots -2,1,6, we can express f(x) as f(x)=(x+2)(x-1)(x-6)*g(x), where g(x) is a quadratic function.
f(2)=32=(2+2)(2-1)(2-6)*g(2), so g(2)=-2
We have two cases:
Case 1: ...
This shows how to give an example of a polynomial function with given characteristics.