How do you divide #(x^3-9x^2+27x-28)div(x-3)# using synthetic division?

1 Answer
Jul 11, 2018

Answer:

The remainder is #=(-1)# and the quotient is #=(x^2-6x+9)#

Explanation:

Let's perform the synthetic division

#color(white)(aaaa)##3##|##color(white)(aaaa)##1##color(white)(aaaa)##-9##color(white)(aaaaaa)##27##color(white)(aaaaa)##-28#

#color(white)(aaaaa)##|##color(white)(aaaa)##color(white)(aaaaaa)##3##color(white)(aaaaa)##-18##color(white)(aaaaaa)##27#

#color(white)(aaaaaaaaa)###_________________________________________________________##

#color(white)(aaaaa)##|##color(white)(aaaa)##1##color(white)(aaaa)##-6##color(white)(aaaaaaa)##9##color(white)(aaaaa)##color(red)(-1)#

The remainder is #=(-1)# and the quotient is #=(x^2-6x+9)#

Therefore,

#(x^3-9x^2+27x-28)/(x-3)=x^2-6x+9-(1)/(x-3)#