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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 ) .

User FanoFN
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2 Answers

7 votes

Answer:

the missing dimension is (4x-11).

User ItsAmy
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3 votes

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).

User Dato Gogshelidze
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