How do you find the quotient of #(h^3+2h^2-3h+9)/(h+3)# using synthetic division?

1 Answer
Jul 5, 2018

Answer:

The remainder is #9# and the quotient is #=h^2-h#

Explanation:

Let's perform the synthetic division

#color(white)(aaaa)##-3##|##color(white)(aaaa)##1##color(white)(aaaaa)##2##color(white)(aaaaaa)##-3##color(white)(aaaaaaa)##9#

#color(white)(aaaaaaa)####|##color(white)(aaaa)####color(white)(aaaa)##-3##color(white)(aaaaaaa)##3##color(white)(aaaaaaa)##0#

#color(white)(aaaaaaaaa)###_________________________________________________________##

#color(white)(aaaaaaa)####|##color(white)(aaaa)##1##color(white)(aaa)##-1##color(white)(aaaaaaa)##0##color(white)(aaaaaaa)##color(red)(9)#

The remainder is #9# and the quotient is #=h^2-h#

Therefore,

#(h^3+2h^2-3h+9)/(h+3)=(h^2-h)+9/(h+3)#