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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.