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 the width, x, in feet. Enter the equation in the field by replacing the values of a, b, c, and d.

y = ax^3 + bx^2 + cx + d

Answer 1

y=x^3+8x^2-20+0

Explanation:

x(x-2)(x+10)

x= width x-2= height x+10=length

Distribute x

(x^2-2x)(x+10)

Use FOIL method

x^3 + 10x^2 - 2x^2 -20x

Simplify

x^3 + 8x^2 - 20x + 0

Therefore y=x^3+8x^2-20+0

(Got correct in Plato :) )

Answer 2

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