How do you use long division to divide #(x^3-9)div(x^2+1)#?

1 Answer
Jun 25, 2017

The quotient is #x# and the remainder is #=-(x+9)#

Explanation:

Let's perform the long division

#color(white)(aaaa)##x^2+1##color(white)(aaaa)##|##x^3##color(white)(aaaa)##+0x^2##color(white)(aaaa)##+0x##color(white)(aaaa)##-9##color(white)(aaaa)##|##x#

#color(white)(aaaa)##color(white)(aaaaaaaaaaa)##x^3##color(white)(aaaa)##color(white)(aaaaaaaaa)##+x##color(white)(aaaa)#

#color(white)(aaaa)##color(white)(aaaaaaaaaaa)##0##color(white)(aaaa)##color(white)(aaaaaaaaaa)##-x##color(white)(aaaa)##-9#

The quotient is #x# and the remainder is #=-(x+9)#

#(x^3-9)/(x^2+1)=x-(x+9)/(x^2+1)#