How do you find the quotient of #(2-x+x^2-x^3-x^4)div(x+2)# using synthetic division?

1 Answer
Jun 29, 2018

Answer:

The remainder is #0# and the quotient is #=-x^3+x^2-x+1#

Explanation:

Let's perform the synthetic division

#color(white)(aaaa)##-2##|##color(white)(aaaa)##-1##color(white)(aaaa)##-1##color(white)(aaaaaa)##1##color(white)(aaaa)##-1##color(white)(aaaaaa)##2#

#color(white)(aaaaaaa)####|##color(white)(aaaa)####color(white)(aaaaaaaa)##2##color(white)(aaaaa)##-2##color(white)(aaaaa)##2##color(white)(aaaa)##-2#

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

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

The remainder is #0# and the quotient is #=-x^3+x^2-x+1#