Question

How do you simplify and divide `(x^3+13x^2-12x-8)/(x+2)`?

Answer 1

Quotient is `x^2+11x-34` and remainder is `60`

Explanation:

To divide `x^3+13x^2-12x-8` by `x+2`

One Write the coefficients of `x` in the dividend inside an upside-down division symbol.

`color(white)(1)|color(white)(X)1" "color(white)(X)13color(white)(XX)-12" "" "-8`
`color(white)(1)|" "color(white)(X)`
`" "stackrel("—————————————)`

Two As `x+2=0` gives `x=-2` put `-2` at the left.

`-2|color(white)(X)1" "color(white)(X)13color(white)(Xx)-12" "" "2`
`color(white)(xx)|" "color(white)(XX)`
`" "stackrel("—————————————)`

Three Drop the first coefficient of the dividend below the division symbol.

`-2|color(white)(X)1" "color(white)(X)13color(white)(XX)-12" "" "-8`
`color(white)(xx)|" "color(white)(X)`
`" "stackrel("—————————————)`
`color(white)(xx)|color(white)(X)color(red)1`

Four Multiply the result by the constant, and put the product in the next column.

`-2|color(white)(X)1" "color(white)(X)13color(white)(XX)-12" "" "-8`
`color(white)(xx)|" "color(white)(Xx)-2`
`" "stackrel("—————————————)`
`color(white)(xx)|color(white)(X)color(blue)1`

Five Add down the column.

`-2|color(white)(X)1" "color(white)(X)13color(white)(XX)-12" "" "-8`
`color(white)(xx)|" "color(white)(Xx)-2`
`" "stackrel("—————————————)`
`color(white)(xx)|color(white)(X)color(blue)1color(white)(X11)color(red)11`

Six Repeat Steps Four and Five until you can go no farther.

`-2|color(white)(X)1" "color(white)(X)13color(white)(XX)-12" "" -8`
`color(white)(xx)|" "color(white)(XX)-2color(white)(xx)-22color(white)(Xxx)68`
`" "stackrel("—————————————)`
`color(white)(xx)|color(white)(X)color(blue)1color(white)(X11)color(red)11color(white)(XX)color(red)(-34)color(white)(XXX)color(red)(60)`

Hence, Quotient is `x^2+11x-34` and remainder is `60`.