Question

You are given an expression for the volume of the rectangular prism. Determine an expression for the missing dimension.

Answer 1

Answer:

the missing dimension is (4x-11).

Answer 2

Given:

The volume of the rectangular prism is

$V=4x^3+5x^2-32x-33$

Two dimensions are (x+1) and (x+3).

To find:

The missing dimension.

Solution:

We know that, volume of a rectangular prism is

$V=length\times breadth\times height$

It means, volume of a rectangular prism is the product of all dimensions.

We have,

$V=4x^3+5x^2-32x-33$

Splitting the middle terms, we get

$V=4x^3+4x^2+x^2+x-33x-33$

$V=4x^2(x+1)+x(x+1)-33(x+1)$

$V=(x+1)(4x^2+x-33)$

Splitting the middle term, we get

$V=(x+1)(4x^2+12x-11x-33)$

$V=(x+1)(4x(x+3)-11(x+3))$

$V=(x+1)(x+3)(4x-11)$

So, the three dimensions of the rectangular prism are (x+1), (x+3) and (4x-11).

Therefore, the missing dimension is (4x-11).