Now d=e=f=0 as lim x -0(p(x)/x^3 -2)=4 so power of x<3 causing the destabilisation of finite value on right side.
so our polynomial p(x) becomes p(x)=ax^5+bx^4+cx^3
Now, putting all values in limit and we get c-2=4 implies c=6.
Also p(x) has extremum at -1 and 1 so putting the value firstly x=-1 and equating dp(x)/dx=0.
We get equation (1)
Using same for x=1 and we get equation (2)
Solving equation (1) and (2) we get "a" and "b"
Putting value of "a", "b", "c" in p(x) we get our desired polynomial.