How do you divide #(v^3-10v^2+15v+20)div(v-3)# using synthetic division?

1 Answer
Jun 11, 2017

Answer:

The remainder is #=2# and the quotient is #=v^2-7v-6#

Explanation:

Let's perform the synthetic division

#color(white)(aaaa)##3##color(white)(aaaaa)##|##color(white)(aaaa)##1##color(white)(aaaaaa)##-10##color(white)(aaaaaa)##15##color(white)(aaaaa)##20#
#color(white)(aaaaaaaaaaaa)#_________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaaaaaa)##3##color(white)(aaaaa)##-21##color(white)(aaaa)##-18#
#color(white)(aaaaaaaaaaaa)#________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##1##color(white)(aaaaaa)##-7##color(white)(aaaaa)##-6##color(white)(aaaaaa)##color(red)(2)#

The remainder is #=2# and the quotient is #=v^2-7v-6#

#(v^3-10v^2+15v+20)/(v-3)=v^2-7v-6+2/(v-3)#