(i) Polynomial P (x) = x4 - 4x3 + 4x2 - 1 has the local maximum at (1,0) and local minimum at (0, -1) and (2, -1). Factor polynomial completely and draw graph of it also using local extrema.
(ii) Find how many real zeros polynomial Q(x) = P(x)+c has for different constants c. Adding c is going to shift graph of P(x) up or down depending on value of c.