A box company is designing a new rectangular gift container. The marketing department has designed a box with a width 2 inches shorter than its length and a height 3 inches taller than its length. The volume of the box must be 56 cubic inches. What are the dimensions of the box?

The width is? ... ? inches,

the length is? ... ? inches and the

height is? ... ? inches.

Volume of the box = 56 cubic inches

let x is the length, then

width = 2 inches shorter than its length = x - 2

height = 3 inches taller than its length = x+3

Volume = length x width x height

56 = x x (x-2) x (x+3)

56 = (x ² - 2x) (x+3)

56 = x³ + 3x² - 2x² - 6x

56 = x³ + x² - 6x

x³+x²-6x-56 = 0

using the rational root theorem and factoring the polynomial;

(x-4) (x² + 5x + 14) = 0

from here;

x-4 = 0

x = 4

So, length = 4 inches

width = x - 2 = 4 - 2 = 2 inches

length = x + 3 = 4 + 3 = 7 inches

volume = l x w x h = 4 x 2 x 7 = 56