How do you divide #(x^3+6x^2-30x+102)div(x+10)# using synthetic division?

1 Answer
Oct 23, 2016

Answer:

The result #(x^3+6x^2-30x+102)/(x+10)=(x^2-4x+10)+2/(x+10)#

Explanation:

Let's do the division
#x^3+6x^2-30x+102##color(white)(aaaaa)##∣x+10#
#x^3+10x^2##color(white)(aaaaaaaaaaaaaaa)##∣x^2-4x+10#
#0- 4x^2-30x#
#color(white)(aa)##-4x^2-40x#
#color(white)(aaaaa)##0+10x+102#
#color(white)(aaaaaaaaa)##10x+100#
#color(white)(aaaaaaaaaaa)##0+2#

The remainder #=2#

so the result is #(x^3+6x^2-30x+102)/(x+10)=(x^2-4x+10)+2/(x+10)#