Question

Divide.
(x^2+8x+12)/(x+5)

Answer 1

`x^2+8x+12=(x+5)(x+3)-3.`

The quotient is
`x+3` and the remainder is -3.

Explanation:

Dividing
`x^2+8x+12` by
`x+5,` multiply
`x+5` by x:

`(x+5)x=x^2+5x` and subtract it from
`x^2+8x+12:`

`x^2+8x+12-(x^2+5x)=x^2+8x+12-x^2-5x=3x+12.`

Now multiply
`x+5` by 3:

`(x+5)\cdot 3=3x+15`

and subtract it from
`3x+12:`

`3x+12-(3x+15)=3x+12-3x-15=-3.`

Thus,

`x^2+8x+12=(x+5)(x+3)-3.`

The quotient is
`x+3` and the remainder is -3.