Factor completely:

x³ + 4x² -25x - 100

Identify the zeros of the given polynomial function and state their multiplicities. Describe also how the graph behaves with the x-axis.

f(x) = x³ + 8x² - 9x - 72

For the following function, graph and identify its domain's open intervals for which the function is increasing or decreasing. f(x) = (1/5)(x + 5)⁴ - 5

For the following polynomial function, determine whether the real zero satisfies the given condition or not.

f(x) = 4x⁵ - 3x⁴ + 5x³ - 7x² + 12x - 11; no real zero greater than 4

A cardboard has a dimension of 100 cm by 70 cm. This will be turned into a storage box by cutting squares from each of its corners and folding up its sides. The squares will be of the same dimensions. Let x be the length, in centimeters, of the side of each square to be cut. Determine the value of x that will maximize the volume of the storage box by using the table feature of a graphing utility. Express your answer in two decimal places.