For each polynomial function, complete the following in order.

(a) Use Descartes’ rule of signs to determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros.

(b) Use the rational zeros theorem to determine the possible rational zeros.

(c) Find the rational zeros, if any.

(d) Find all other real zeros, if any.

(e) Find any other complex zeros (that is, zeros that are not real), if any.

(f) Find the x-intercepts of the graph, if any.

(g) Find the y-intercept of the graph.

(h) Use synthetic division to find ƒ(4), and give the coordinates of the corresponding point on the graph.

(i) Determine the end behavior of the graph.

(j) Sketch the graph.

ƒ(x) = 4x⁵ + 8x⁴ + 9x³ + 27x² + 27x