Question

How do you divide `(2x^3+2x^2+4x+4)/(x^2+8x+4)`?

Answer 1

`(color(blue)(2x^3+2x^2+4x+4))/color(red)(x^2+8x+4)=color(green)((2x-14))+(108x+60)/color(red)(x^2+8x+4)`

Explanation:

Here ,

Dividend `:color(blue)(2x^3+2x^2+4x+4) and`

divisor `: color(red)(x^2+8x+4)`

So ,

`color(white)(..................................)color(green)(ul(2x-14color(white)(.........))larrquotient`
`color(white)(..........)color(red)((x^2+8x+4))` `|color(blue)(2x^3+2x^2+4x+4)` ##

`color(white)()color(violet)((color(red)(x^2+8x+4))*2xtocolor(white)()ul(2x^3+16x^2+8x)` `color(white)(.......)lArr"subtract"`
`color(white)(.....................................)-14x^2-4x+4`

`color(white)()color(violet)((color(red)(x^2+8x+4))(-14)tocolor(white)()ul(-14x^2-112x-56)` `color(white)(.......)lArr"subtract"`
`color(white)(..........................................)color(green)(` `color(white)(.........)108x+60larr"Remainder"`

Hence ,

`(color(blue)(2x^3+2x^2+4x+4))`=`(color(red)(x^2+8x+4))(2x-14)+(108x+60)`

`Quotient :q(x)=color(green)(2x-14` `"and Remainder " :r(x)=108x+60`