Which of the following describe the roots the polynomial f(x)=(x+2)^2(x-4)(x+1)^3?

There are exactly 6 roots of the polynomial and they are -2, -2, 4, -1, -1, -1. 

We know that there are 6 because it is a 6th power polynomial and there will always be the same number of root as the power of the polynomial. 

Also, we can expand this polynomial to more easily see the roots. 

f(x) = (x + 2)(x + 2)(x - 4)(x + 1)(x +1)(x + 1)

Now we can set each parenthesis equal to 0 and solve in order to get each root. There is an example below for you.

x + 2 = 0 ---> subtract 2 from each side
x = -2

So your first root is -2. Then repeat for the rest.