Score for Question 2: ___ of 40 points)

Question

For the polynomial (x)=x^5-5x^4+12x^3-24x^2+32x-16 , answer the following questions. Show all of your work.
How many zeros does the function have over the set of complex numbers?
What is the maximum number of local extrema (maxima or minima) the graph of the function can have?
Complete the following statements:

List the possible rational zeros of this function.
Factor this polynomial completely over the set of complex numbers.

Answer 1

linear has 1
quadratic has 2
etc
so five

derivative of quadratic is linear
etc
so 4

http://www.wolframalpha.com/widgets/view.jsp?id=b858339e64fa997454dd12f77cb1ece1
+2i , -2i , 1, 2
(x-2)(x-1)(x^2+4) = (x-2)(x-1)(x-2i)(x+2i)

Answer 2

PS, if it ends in +/-16, try +/-4 and +/-2 :)

Answer 3

Oh, there are two at x = 2 by the way
(x-2)(x-2)(x-1)(x-2i)(x+2i)