Question

How do you long divide `((x^5)-4(x^4)+(x^3)-7x+1 )/( x+2)`?

Answer 1

`x^2-6x^3+13x^2-26x+45-89/(x+2)`

Explanation:

Toa maintain positioning logic (lining up) I introduce place holders such as `0x^2`

`" "x^5-4x^4+x^3+0x^2-7x+1`
`color(magenta)(x^4)(x+2)->" " ul(x^5+2x^4color(white)(.........) larr" "Subtract)`
`" "0-6x^4+x^3+0x^2-7x+1`
`color(magenta)(-6x^3)(x+2)-> ul(-6x^4-12x^3color(white)(.........) larr" "Subtract)`
`" "0+13x^3+0x^2-7x+1`
`color(magenta)(13x^2)(x+2)-> " "ul(13x^3+26x^2" "larr Subtract)`
`" "0-26x^2-7x+1`
`color(magenta)(-26x)(x+2)->" "ul(-26x^2-52x" "larr Subtract)`
`" "0+45x+1`
`color(magenta)(45)(x+2)->" "ul(45x+90" "larr Subtr.`
`" "0color(magenta)(-89)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(magenta)(x^2-6x^3+13x^2-26x+45-89/(x+2))`