# Polynomial Geometry Question?

I was wondering if anybody could help me with this?

A rectangular prism has a volume of 1050cm^3. If the height of the prism is 3 cm less the width of the base, and the length of the base is 5 cm grater than the width of the base, find the dimensions of the rectangular prism. Solve Algebraically. Relevance

A rectangular prism has a volume of 1050 cm^3.

If the height of the prism is 3 cm less than the width of the base,

and the length of the base is 5 cm greater than the width of the base,

find the dimensions of the rectangular prism.

If the width of the base of the prism is 'w'

its length is '(w + 4)', and its height is '(w - 3)'.

The volume of the prism is -12 w + w^2 + w^3

w^3 + w^2 - 12 w - 1050 = 0

The width of the prism ≈ 10.222

The length of the prism ≈ 14.222

and

the height of the prism w ≈ 7.222

Three consecutive integers with a product of -336:

(x - 1) × x × (x + 1) = -336

x^3 - x + 336 = 0

(x + 7) (x^2 - 7 x + 48) = 0

-8, -7, and -6 are the three consecutive integers.

• Let width be x the height be x-3 and its length be x+5

Volume of rectangular prism (x)(x-3)(x+5) = 1050cm^3

Solving the equation: x = 10

Dimensions: width = 10 cm, height = 7 cm and length = 15 cm

Check: 10*7*15 = 1050 cubic cm