Question

What is the volume of the box expressed as a polynomial?

2x-1 5x-4 x+4

A.) 10x^2 - 32x + 4
B.) 10x^3 - 27x^2 - 32x + 16
C.) 10x^3 - 16
D.) 10x^3 + 27x^2 - 48x + 16

Answer 1

You have to multiply the polynomials by each other:
(2x-1) * (5x-4) =10x^2-13x+4
(10x^2-13x+4)(x+4)=

10x^3+27x^2-48x+16

Answer 2

D.
`10x^3+27x^2-48x+16`

Explanation:

We have been given lengths of a box as:
`(2x-1),(5x-4)\text { and }(x+4)`. We are asked to find the volume of our given box.

Since all the sides of box are not equal, therefore, our box is a rectangular box.

Since the volume of a rectangular box equals the product of all of its sides, so we will multiply our given sides to find the volume of box as:

`(2x-1)(5x-4)(x+4)`

First of all we will multiply our first two expressions as:

`(2x-1)(5x-4)=2x*5x-2x*4-1*5x-1*-4`

`(2x-1)(5x-4)=10x^2-8x-5x+4`

`(2x-1)(5x-4)=10x^2-13x+4`

Now we will multiply
`(10x^2-13x+4)` with
`(x+4)`.

`(10x^2-13x+4)(x+4)`

`10x^2*x+10x^2*4-13x*x-13x*4+4*x+4*4`

`10x^3+40x^2-13x^2-52x+4x+16`

`10x^3+27x^2-48x+16`

Therefore, the volume of our given box is
`10x^3+27x^2-48x+16` cubic units and option D is the correct choice.