How do you use long division to divide (x^3-9)div(x^2+1)(x39)÷(x2+1)?

1 Answer
Jun 25, 2017

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

Explanation:

Let's perform the long division

color(white)(aaaa)aaaax^2+1x2+1color(white)(aaaa)aaaa|x^3x3color(white)(aaaa)aaaa+0x^2+0x2color(white)(aaaa)aaaa+0x+0xcolor(white)(aaaa)aaaa-99color(white)(aaaa)aaaa|xx

color(white)(aaaa)aaaacolor(white)(aaaaaaaaaaa)aaaaaaaaaaax^3x3color(white)(aaaa)aaaacolor(white)(aaaaaaaaa)aaaaaaaaa+x+xcolor(white)(aaaa)aaaa

color(white)(aaaa)aaaacolor(white)(aaaaaaaaaaa)aaaaaaaaaaa00color(white)(aaaa)aaaacolor(white)(aaaaaaaaaa)aaaaaaaaaa-xxcolor(white)(aaaa)aaaa-99

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

(x^3-9)/(x^2+1)=x-(x+9)/(x^2+1)x39x2+1=xx+9x2+1