How do you divide #(x^4+5x^3-2x^2-4x+4)div(x+3)# using synthetic division?

1 Answer
Sep 1, 2017

Answer:

The remainder is #color(red)(-56)# and the quotient is #=x^3+2x^2-8x+20#

Explanation:

Let's perform the synthetic division

#color(white)(aa)##-3##color(white)(aaaaa)##|##color(white)(aaa)##1##color(white)(aaaaaaaa)##5##color(white)(aaaaaa)##-2##color(white)(aaaa)##-4##color(white)(aaaaaa)##4#
#color(white)(aaaaaaaaaaaa)##------------#

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaaa)##-3##color(white)(aaaaaa)##-6##color(white)(aaaaa)##24##color(white)(aaaa)##-60#
#color(white)(aaaaaaaaaaaa)##------------#

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aa)##1##color(white)(aaaaaaaa)##2##color(white)(aaaaaa)##-8##color(white)(aaaaa)##20##color(white)(aaa)##color(red)(-56)#

The remainder is #color(red)(-56)# and the quotient is #=x^3+2x^2-8x+20#

#(x^4+5x^3-2x^2-4x+4)/(x+3)=x^3+2x^2-8x+20-56/(x+3)#