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
1 answer:
Prism is a polyhedron that has two parallel polygonal faces. The area of the base can be written as (x-2)(2x+9).
<h3>What is the prism?</h3>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,
Thus, the division of the polynomial can be written as,
Hence, the area of the base can be written as (x-2)(2x+9).
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