Question

How do you divide `(x^3+5x^2+7x+2)div(x+2)` using synthetic division?

Answer 1

Quotient is `x^2+3x+1` and remainder is `0`

Explanation:

To divide `x^3+5x^2+7x+2` 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)5color(white)(XX)7" "" "2`
`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)5color(white)(XX)7" "" "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)5color(white)(XX)7" "" "2`
`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)5color(white)(XX)7" "" "2`
`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)5color(white)(XX)7" "" "2`
`color(white)(xx)|" "color(white)(Xx)-2`
`" "stackrel("—————————————)`
`color(white)(xx)|color(white)(X)color(blue)1color(white)(X11)color(red)3`

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

`-2|color(white)(X)1" "color(white)(X)5color(white)(XX)7" "" "2`
`color(white)(xx)|" "color(white)(X)-2color(white)(X)-6color(white)(X)-2`
`" "stackrel("—————————————)`
`color(white)(xx)|color(white)(X)color(blue)1color(white)(X11)color(red)3color(white)(XX)color(red)1color(white)(XXX)color(red)0`

Hence, Quotient is `x^2+3x+1` and remainder is `0`.