How do you find the quotient of #(2s^3+3s^2-9s-10) div (s-2)# using synthetic division?

1 Answer
May 20, 2017

Answer:

The quotient is #=2s^2+7s+5#

Explanation:

Let's perform the synthetic division

#color(white)(aaaa)##2##color(white)(aaaaa)##|##color(white)(aaaa)##2##color(white)(aaaaaa)##3##color(white)(aaaaaa)##-9##color(white)(aaaa)##-10#
#color(white)(aaaaaaaaaaaa)#_________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaaaa)##4##color(white)(aaaaaaa)##14##color(white)(aaaaa)##10#
#color(white)(aaaaaaaaaaaa)#________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##2##color(white)(aaaaa)##7##color(white)(aaaaaaaa)##5##color(white)(aaaaaa)##color(red)(0)#

#(2s^3+3s^2-9s-10)/(s-2)=(2s^2+7s+5)#

The remainder is #=0# and the quotient is #=2s^2+7s+5#