Question

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

Answer 1

`x^3+5x-14+26/(x+2)`

Explanation:

I'd like to use synthetic division for `color(red)(1)x^4+color(blue)(2)x^3+color(purple)(5)x^2+color(green)(-4)x+color(orange)(-2)`

`color(black)(-2)color(black)(|)color(red)(1)color(white)(-)color(blue)(2)color(white)(-)color(purple)(5)color(white)(.)color(green)(-4)color(white)(.)color(orange)(-2)`
`color(white)(-2)color(black)(|)color(white)(1)color(white)(.)color(black)(-2)color(white)(-)color(black)(0)color(white)(.)color(black)(-10)color(white)(.)color(black)(28)`
`color(white)(-2.)..........................................`
`color(white)(-2)color(black)(|)color(black)(1)color(white)(-)color(black)(0)color(white)(-)color(black)(5)color(white)(.)color(black)(-14)color(white)(.)color(black)(26)`

We have a remainder, but that's not a problem :)

`x^3+0x^2+5x-14+26/(x+2)`
`x^3+5x-14+26/(x+2)`