Consider the function f(x) = x^4 - x^3 - 3x^2 + x + 2

(a) Use the rational zeros theorem and long division to factor completely.

(b) State the x and y intercepts of the graph of f(x)

(c) Describe the behavior of the polynomial at the intercepts

(d) State the end behavior of f(x)

(e) Sketch a graph of f(x) that incorporates all of the above information.

1. What is a polynomial function g(x) that has the following properties (be sure to explicitely verify that it has the desired properties

(a) The zeros of f(x) are x=-2, x=3, x=5

(b) (3, 0) is a local minimum of f(x)

(c) As x -> , f(x) -> - ;

(d) As x -> - , f(x) ->