Question

How do you find the quotient of `(m^4-2m^3+m^2+12m-6)/(m-2)` using synthetic division?

Answer 1

Quotient `color(green)(Q = m^2 + m + 14)`, Remainder `color(green)(R = 22 / (m-2))`

Explanation:

Synthetic Division :

`color(white)(aa)2color(white)(aa)|color(white)(aa)1color(white)(aa)-2color(white)(aa)1color(white)(aa)12color(white)(aa)-6`
`color(white)(aaaaa)|color(white)(a)darrcolor(white)(aaaa)2color(white)(aa)0color(white)(aaa)2color(white)(aaa)28`
`color(white)(aaaaa)----------`
`color(white)(aaaaaaaaa)1color(white)(aaaa)0color(white)(aa)1color(white)(aaa)14color(white)(aaa)22`

Quotient `color(green)(Q = m^2 + m + 14)`, Remainder `color(green)(R = 22 / (m-2))`