How do you divide #(2x^3-11x^2+9x-20)div(x-5)# using synthetic division?

1 Answer
Aug 13, 2017

Answer:

The remainder is #color(red)(0)# and the quotient is #=2x^2-x+4#

Explanation:

Let's perform the synthetic division

#color(white)(aaaa)##5##color(white)(aaaaaa)##|##color(white)(aa)##2##color(white)(aaaaaaa)##-11##color(white)(aaaaaa)##9##color(white)(aaaaaaa)##-20#
#color(white)(aaaaaaaaaaaa)##------------#

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaaaaa)##10##color(white)(aaaaaa)##-5##color(white)(aaaaaaaa)##20#
#color(white)(aaaaaaaaaaaa)##------------#

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaa)##2##color(white)(aaaaaa)##-1##color(white)(aaaaaaaa)##4##color(white)(aaaaaaaa)##color(red)(0)#

The remainder is #color(red)(0)# and the quotient is #=2x^2-x+4#

#(2x^3-11x^2+9x-20)/(x-5)=2x^2-x+4#