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

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

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Answer 1 · 2018-07-05T07:50:49

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

Explanation:

Let's perform the synthetic division

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

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

$a a a a a a a a a$ $color(white)(aaaaaaaaa)$ _________________________________________________________##

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

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

Therefore,

$\frac{h^{3} + 2 h^{2} - 3 h + 9}{h + 3} = (h^{2} - h) + \frac{9}{h + 3}$ $(h^3+2h^2-3h+9)/(h+3)=(h^2-h)+9/(h+3)$

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

1 Answer

Explanation:

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How do you find the quotient of h3+2h2−3h+9h+3(h^3+2h^2-3h+9)/(h+3) using synthetic division?

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Explanation:

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