Consider the polynomial h(x)=x4−5x3+6x2. Answer the following:
(a) Factorise h(x) completely over the real numbers.
(b) Determine the maximum number of real x-intercepts that the graph of h can have, giving a brief reason for your answer.
(c) Find all x-intercepts and the y-intercept of h.
(d) Using only the intercepts found in part (iii), sketch a rough graph of h(x) on your answer sheet and clearly label all intercepts.