Question

How do you divide `(r^2+6r+15)div(r+5)` using synthetic division?

Answer 1

Remainder is `10` and `(r^2+6r+15)-:(r+5)=r+1+10/(r+5)`

Explanation:

To divide `r^2+6r+15` by `r+5`

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

`color(white)(1)|color(white)(X)1" "color(white)(X)6color(white)(XX)15`
`color(white)(1)|" "color(white)(X)`
`" "stackrel("—————————————)`

Two Put the divisor at the left (as it is `r+5`, we need to put `-5`.

`-5|color(white)(X)1" "color(white)(X)6color(white)(XX)15`
`color(white)(Xx)|" "color(white)(X)`
`" "stackrel("—————————————)`

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

`-5|color(white)(X)1" "color(white)(X)6color(white)(XX)15`
`color(white)(xx)|" "color(white)(X)`
`" "stackrel("—————————————)`
`color(white)()(1)|color(white)(X)color(red)1`

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

`-5|color(white)(X)1" "color(white)(X)6color(white)(XX)15`
`color(white)(221)|" "color(white)(X)-5`
`" "stackrel("—————————————)`
`color(white)(221)|color(white)(X)color(blue)1`

Five Add down the column.

`-5|color(white)(X)1" "color(white)(X)6color(white)(XX)15`
`color(white)(221)|" "color(white)(X1)-5`
`" "stackrel("—————————————)`
`color(white)(221)|color(white)(X)color(blue)1color(white)(XX)color(red)1`

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

`2|color(white)(X)1" "color(white)(X)6color(white)(XX)15`
`color(white)(1)|" "color(white)(X1)-5color(white)(X)-5`
`" "stackrel("—————————————)`
`color(white)(1)|color(white)(X)color(blue)1color(white)(X11)color(red)1color(white)(XX)color(red)10`

Remainder is `10` and

`(r^2+6r+15)-:(r+5)=r+1+10/(r+5)`