How do you divide #(x^3+x^2-17x+15)div(x+5)# using synthetic division?

1 Answer
Jul 20, 2017

Answer:

The remainder is #0# and the quotient is #=x^2-4x+3#

Explanation:

Let's perform the synthetic division

#color(white)(aaaa)##-5##color(white)(aaaa)##|##color(white)(aaaa)##1##color(white)(aaaa)##1##color(white)(aaaaaa)##-17##color(white)(aaaaaaa)##15#
#color(white)(aaaaaaaaaaaa)#_________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaa)##-5##color(white)(aaaaaaa)##20##color(white)(aaaaaa)##-15#
#color(white)(aaaaaaaaaaaa)#________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaa)##1##color(white)(aaa)##-4##color(white)(aaaaaaaa)##3##color(white)(aaaaaaaa)##color(red)(0)#

The remainder is #color(red)(0)# and the quotient is #=x^2-4x+3#

#(x^3+x^2-17x+15)/(x+5)=x^2-4x+3#