How do you use synthetic division to divide #(5x^3+6x+8)div(x+2)#?

1 Answer
Apr 1, 2017

Answer:

The quotient is #=5x^2-10x+26# and the remainder is #=-44#

Explanation:

Let #f(x)=5x^3+6x+8#

Let's perform the synthetic division

#color(white)(aaaa)##-2##color(white)(aaaaa)##|##color(white)(aaaa)##5##color(white)(aaaa)##0##color(white)(aaaAAAa)##6##color(white)(aaAaa)##8#
#color(white)(aaaaaaaaaaaa)#________

#color(white)(aaaa)####color(white)(aaaaaaa)##|##color(white)(aaaa)####color(white)(aaaa)##-10##color(white)(aaaaa)##20##color(white)(aaa)##-52#
#color(white)(aaaaaaaaaaaa)#________
#color(white)(aaaa)####color(white)(aaaaaaa)##|##color(white)(aaaa)##5##color(white)(aaa)##-10##color(white)(aaaaa)##26##color(white)(aaa)##color(red)(-44)#

#f(x)=(x+2)(5x^2-10x+26)-44#