How do you divide $(x^3-9x^2+27x-28)div(x-3)$ using synthetic division?

Question

2092 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-11T14:47:07

The remainder is $=(-1)$ and the quotient is $=(x^2-6x+9)$

$color(white)(aaaa)$ $3$ $|$ $color(white)(aaaa)$ $1$ $color(white)(aaaa)$ $-9$ $color(white)(aaaaaa)$ $27$ $color(white)(aaaaa)$ $-28$

$color(white)(aaaaa)$ $|$ $color(white)(aaaa)$ $color(white)(aaaaaa)$ $3$ $color(white)(aaaaa)$ $-18$ $color(white)(aaaaaa)$ $27$

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

$color(white)(aaaaa)$ $|$ $color(white)(aaaa)$ $1$ $color(white)(aaaa)$ $-6$ $color(white)(aaaaaaa)$ $9$ $color(white)(aaaaa)$ $color(red)(-1)$

The remainder is $=(-1)$ and the quotient is $=(x^2-6x+9)$

Therefore,

$(x^3-9x^2+27x-28)/(x-3)=x^2-6x+9-(1)/(x-3)$

How do you divide (x^3-9x^2+27x-28)div(x-3)(x^3-9x^2+27x-28)div(x-3) using synthetic division?