Question

Farmer Jim is building a new chicken coop in the shape of a rectangular prism. He needs the height of the coop to be 2 feet shorter than the width, and needs the length of the coop to be 10 feet longer than the width. Create an equation to represent the volume of the chicken coop, y, in terms of width, x, in feet.

Answer 1

Let the width of the coop be x. Then the height is x - 2, and the length is x + 10. Then the volume of the coop (a rectangular prism) is:

y = x(x-2)(x+10) = x^3 + 8x^2 - 20x

Based on the given format, this means that:

a = 1

b = 8

c = -20

d = 0