Question

The volume of a rectangular prism is `2x^3+9x^2-8x-36` with height `x+2`. Using synthetic division, what is the area of the base?

Answer 1

The area of the base is `=2x^2+5x-18`

Explanation:

Let's do the long division

`color(white)(aaaa)` `2x^3+9x^2-8x-36` `color(white)(aaaa)` `∣` `x+2`

`color(white)(aaaa)` `2x^3+4x^2` `color(white)(aaaaaaaaaaaaa)` `∣` `2x^2+5x-18`

`color(white)(aaaaaa)` `0+5x^2-8x`

`color(white)(aaaaaaaa)` `+5x^2+10x`

`color(white)(aaaaaaaaaa)` `+0-18x-36`

`color(white)(aaaaaaaaaaaaaa)` `-18x-36`

`color(white)(aaaaaaaaaaaaaaaa)` `-0-0`

The remainder is `=0`

The quotient is `=2x^2+5x-18`