How do you divide #(p^5+5p^3-11p^2-25p+29)div(p+6)# using synthetic division?

1 Answer
Jun 25, 2017

Answer:

The remainder is #=-9073# and the quotient is #=p^4-6p^3+41p^2-257p+1517#

Explanation:

Let's perform the synthetic division

#color(white)(aaaa)##-6##color(white)(aaaa)##|##color(white)(aaaa)##1##color(white)(aaaa)##0##color(white)(aaaaa)##5##color(white)(aaaa)##-11##color(white)(aaaa)##-25##color(white)(aaaa)##29#
#color(white)(aaaaaaaaaaaa)#_________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaa)##-6##color(white)(aaaa)##36##color(white)(aaa)##-246##color(white)(aaaa)##1542##color(white)(aa)##-9102#
#color(white)(aaaaaaaaaaaa)#________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##1##color(white)(aa)##-6##color(white)(aaaa)##41##color(white)(aaa)##-257##color(white)(aaaa)##1517##color(white)(aa)##color(red)(-9073)#

The remainder is #=-9073# and the quotient is #=p^4-6p^3+41p^2-257p+1517#

#(p^5+5p^3-11p^2-25p+29)/(p+6)=p^4-6p^3+41p^2-257p+1517-9073/(p+6)#