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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?

2x + 1 and x + 3
2x + 1 and x − 3
2x − 1 and x + 3
2x − 1 and x − 3

Respuesta :

adioabiola

The factors which can represent the length and width of the container are; 2x − 1 and x + 3.

The Volume of a rectangular prism is a three-dimensional quantity and is the product of its length, width and height.

In essence;

  • Volume = l × w × h.

However, V = 2x3 + 5x2 − 3x and height, h = x.

Therefore; V/h = l × w

  • l × w = (2x³ + 5x² - 3x)/x

  • l × w = 2x² + 5x -3.

  • l × w = (2x − 1) (x + 3)

Consequently, the factors which can represent the length and width of the container are; 2x − 1 and x + 3.

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