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?

1 Answer
Dec 13, 2016

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#