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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?

Sagot :

Prism is a polyhedron that has two parallel polygonal faces. The area of the base can be written as (x-2)(2x+9).

What is the prism?

A prism is a polyhedron that has two polygonal faces lying in parallel planes while the other faces are parallelograms.

As it is given that the volume of the prism is 2x³ + 9x² -8x -36 while its height is x+2, therefore, in order to calculate the area of the base we need to divide the polynomial with the height of the prism.

As we need to divide the polynomial 2x³ + 9x² -8x -36 with x+2, therefore, Using the synthetic division the polynomial is divided as shown below.

The polynomial can be factorized as,

[tex]2x^3+9x^2-8x-36\\\\x^2(2x+9)-4(2x+9)\\\\(x^2-4)(2x+9)\\\\(x+2)(x-2)(2x+9)[/tex]

Thus, the division of the polynomial can be written as,

[tex]\dfrac{2x^3+9x^2-8x-36}{x+2} = \dfrac{(x+2)(x-2)(2x+9)}{(x+2)}=(x-2)(2x+9)[/tex]

Hence, the area of the base can be written as (x-2)(2x+9).

Learn more about Prism:

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