Question

The volume of a rectangular prism is 2 x cubed 9 x squared minus 8 x minus 36 with height x 2. Using synthetic division, what is the area of the base? 2 x cubed 13 x squared 18 x 2 x cubed 5 x squared minus 18 x 2 x squared 13 x 18 2 x squared 5 x minus 18.

Answer 1

The base of the prism is $\rm 2x^2+5x-18$.

To solve the problem we will put the values given to us in the formula of volume of a prism.

Prism

A prism is a 3d shape whose two sides are the base sides which are polygon, with the other faces as parallelograms.

The volume of a rectangular prism is 2x3+9x2-8x-36 with height x + 2.

The volume of a rectangular prism is the product of its base area and height,

$\rm Volume \ of \ prism =Area \times height\\\\ 2x^3+9x^2-8x-36 = Area \times x + 2\\\\Area = \dfrac{ 2x^3+9x^2-8x-36 }{x+2}\\\\ Area = \dfrac{ (2x^2+5x-18)(x+2)}{x+2}\\\\Area = 2x^2+5x-18$

Hence, the base of the prism is $\rm 2x^2+5x-18$.

Learn more about Volume of Prism:

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