Question

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

V equal 4 x to the power of 3 plus 5 x to the power of 2 minus 32 x minus 33 and the dimensions are ( x + 1 ) and ( x + 3 ) .

Answer 1

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* breadth* 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).