How do you use synthetic division to divide #(5x^3-6x^2+8)div(x-4)#?

1 Answer
May 14, 2017

Answer:

The remainder is #=232# and the quotient is #=5x^2+14x+56#

Explanation:

Let's perform the synthetic division

Let #f(x)=5x^3-6x^2+8#

Let's perform the synthetic division

#color(white)(aaaa)##4##color(white)(aaaaa)##|##color(white)(aaaa)##5##color(white)(aaaaaa)##-6##color(white)(aaaaaa)##0##color(white)(aaaaaaa)##8#
#color(white)(aaaaaaaaaaaa)#_________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaaaaa)##20##color(white)(aaaaaa)##56##color(white)(aaaaa)##224#
#color(white)(aaaaaaaaaaaa)#________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##5##color(white)(aaaaa)##14##color(white)(aaaaaaa)##56##color(white)(aaaaa)##color(red)(232)#

#f(x)=(5x^2+14x+56)+232/(x-4)#

The remainder is #=232#