Question

How do you divide `(7x^4 -5x^3-5x^2+x-2)/((x + 4) )`?

Answer 1

`7x^3-33x^2+127x+507-2030/(x+4)`

Explanation:

`" "7x^4-color(white)(2)5x^3-5x^2+x-2`
`color(red)(7x^3)(x+4) -> ul(7x^4+28x^3) larr" subtract"`
`" "0color(white)(x^2) -33x^3-color(white)(13)5x^2+x-2`
`color(red)(-33x^2)(x+4) ->ul(color(white)(.)-33x^3-132x^2) larr" subtract"`
`" "0+ 127x^2+" "x-2`
`color(red)(127x)(x+4)->ul(" "127x^2+508x) larr" subtract"`
`" "0-507x-color(white)(202)2`
`color(red)(507)(x+4)->ul(" " -507x+2028 ) larr" sub."`
`" "0" " color(green)(-2030)`

The `color(green)(-2030)` is a remainder so putting it all together we have:

`color(red)(7x^3-33x^2+127x+507)color(green)(-2030/(x+4))`