How do you divide #(x^3-x^2-14x+25)div(x-3)# using synthetic division?

1 Answer
May 19, 2017

Answer:

The remainder is #=1# and the quotient is #=x^2+2x-8#

Explanation:

Let's perform the synthetic division

#color(white)(aaaa)##3##color(white)(aaaaa)##|##color(white)(aaaa)##1##color(white)(aaaaaa)##-1##color(white)(aaaaaa)##-14##color(white)(aaaaaaa)##25#
#color(white)(aaaaaaaaaaaa)#_________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaaaaaa)##3##color(white)(aaaaaaaa)##6##color(white)(aaaaa)##-24#
#color(white)(aaaaaaaaaaaa)#________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##1##color(white)(aaaaaaa)##2##color(white)(aaaaaaa)##-8##color(white)(aaaaaaa)##color(red)(1)#

#(x^3-x^2-14x+25)/(x-3)=(x^2+2x-8)+1/(x-3)#

The remainder is #=1# and the quotient is #=x^2+2x-8#