Question

How do you long divide `(x^3 + 9x^2 + 7x + 3 ) div (x+2)`?

Answer 1

`x^2 +7x-7 +17/(x+2)`

Explanation:

Given: `y=color(red)(1)x^3+color(red)(9)x^2+color(red)(7)x+color(red)(3)`

`-2` |`[(color(white)(0)1, color(white)(00)9, color(white)(000)7, 3)]`
`color(white)(-2)` |`[(color(white)(0)0, -2, -14, 14)]`
`color(white)(-2)` |`[(color(white)(0)1, color(white)(00)7, -7, color(white)(0)17)]`
`x^2 +7x-7 +17/(x+2)`

Answer 2

Quotient`=x^2+7x-7`
Remainder`=17`

Explanation:

`x+2 ) bar(x^3+9x^2+7x+3)(x^2+7x-7`
`color(white)(IiW)ul(_x^3+-2x^2)`
`color(white)(WWWW)7x^2+7x`
`color(white)(WWW)ul(_7x^2+-14x)`
`color(white)(WWWIWW)-7x+3`
`color(white)(WWWWIW)-7x-14`
`color(white)(WWWWTW)ul(+color(white)(W)+color(white)(WW)`
`color(white)(WWWWWWWWW)17`

Quotient`=x^2+7x-7`
Remainder`=17`