How do you divide #(y^4-8y^3+10y^2+2y+4)div(y-2)# using synthetic division?

1 Answer
Jul 26, 2017

Answer:

The remainder is #color(red)(0)# and the quotient is #=y^3-6y^2-2y-2#

Explanation:

Let's perform the [synthetic division]

#color(white)(aaaa)##2##color(white)(aaaaaa)##|##color(white)(aa)##1##color(white)(aaaa)##-8##color(white)(aaaaaa)##10##color(white)(aaaaaaa)##2##color(white)(aaaaaaa)##4#
#color(white)(aaaaaaaaaaaa)#_________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaaa)##2##color(white)(aaaa)##-12##color(white)(aaaaa)##-4##color(white)(aaaaaa)##-4#
#color(white)(aaaaaaaaaaaa)#________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaa)##1##color(white)(aaa)##-6##color(white)(aaaaa)##-2##color(white)(aaaaaa)##-2##color(white)(aaaaaaa)##color(red)(0)#

The remainder is #color(red)(0)# and the quotient is #=y^3-6y^2-2y-2#

#(y^4-8y^3+10y^2+2y+4)/(y-2)=y^3-6y^2-2y-2#