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

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Answer 1 · 2018-07-05T07:50:49

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

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

$color(white)(aaaaaaa)$ #|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,

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

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