How do you use synthetic division to divide #(9x^3-16x-18x^2+32)div(x-2)#?

1 Answer
Apr 2, 2017

Answer:

The quotient is #=9x^2-16# and the remainder is #=0#

Explanation:

Let #f(x)=9x^3-18x^2-16x+32#

Let's perform the synthetic division

#color(white)(aaaa)##2##color(white)(aaaaa)##|##color(white)(aaaa)##9##color(white)(aaaa)##-18##color(white)(aaa)##-16##color(white)(aaaaa)##32#
#color(white)(aaaaaaaaaaaa)#_________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaaaa)##18##color(white)(aaaaa)##0##color(white)(aaaa)##-32#
#color(white)(aaaaaaaaaaaa)#________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##9##color(white)(aaaaaa)##0##color(white)(aaa)##-16##color(white)(aaaaa)##color(red)(0)#

#f(x)=(x-2)(9x^2-16)+0#