Question

Use synthetic division to find the expression for the area of the base of a rectangular prism with height x 4 and volume x3 2x2 – 17x – 36. 2x2 – 9x x2 6x – 24 x2 – 2x – 9 –4x2 8x 36

Answer 1

The expression for the area of the base of Prism is   x2 – 2x – 9

The volume of a rectangular prism is this

Volume = Area x Height

Substituting the given expressions

x3 + 2x2 - 17x - 36 = Area x (x + 4)

Area = (x3 + 2x2 - 17x - 36) / (x + 4)

Now, let's use synthetic division

-4 |    1    2    -17   -36

----    __-4___8___36

        1    -2     -9     0

The expression for the area is

Area = x2 - 2x - 9

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