Question

The volume of a rectangular prism box can be represented by the function V(x) = 2x3 + 5x2 − 3x. If the height of the box is x cm, which of the following can represent the length and width of the container?

Answer 1

The volume of a box is the amount of space in the box.

The expressions that can represent the length and the width are: $\mathbf{(2x - 1)\ and\ (x + 3)}$

The volume is given as:

$\mathbf{V(x) =2x^3 + 5x^2 - 3x}$

Divide through by height (i.e x), to get the base area

$\mathbf{A(x) =2x^2 + 5x - 3}$

Expand

$\mathbf{A(x) =2x^2 + 6x - x - 3}$

Factorize

$\mathbf{A(x) =2x(x + 3) - 1(x + 3)}$

Factor out x + 3

$\mathbf{A(x) =(2x - 1) (x + 3)}$

Hence, the expressions that can represent the length and the width are: $\mathbf{(2x - 1)\ and\ (x + 3)}$

Read more about volumes at:

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