Question

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

Answer 1

Have a look at https://socratic.org/s/aubpbqz9. Not the same values but the process is the same. Unless I have gone wrong, your answer should be:
`" Corrected solution"-> x^4+2x^3+3x^2+6x+11 +17/(x-2)`

Explanation:

Using place holders such as `0x^2` which is the same as `0`

`" "x^4+2x^3+3x^2+6x+11`
`" "x-2bar(|" "color(magenta)(x^5+0x^4-x^3+0x^2-x-5))`
`color(brown)(x^4(x-2)->)" "underline(x^5-2x^4)" " larr" Subtract`
`" "0+2x^4-x^3`
`color(brown)(2x^3(x-2))->" "underline(2x^4-4x^3) larr Subtract`
`" "0+3x^3+0x^2`
`color(brown)(3x^2(x-2))->" "underline(3x^3-6x^2) larr Subtract`
`" "0+6x^2-x`
`color(brown)(6x(x-2))->" "underline(6x^2-12x)`
`" "0+11x-5`
`color(brown)(11(x-2))->" "underline(11x-22)`
`color(brown)(" Remainder") ->" "+17`

`x^4+2x^3+3x^2+6x+11 +17/(x-2)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Check")`

`" "x^4+2x^3+3x^2+6x+11 + 17/(x-2)`

`underline(color(white)(///////////////////////////////////////.)x-2)" "larr "Multiply"`
`x^5+2x^4+3x^2+6x^2+11x`
`underline(0x^5-2x^4-4x^3-6x^2-12x-22+A)" "larr" Add"`
`x^5+" "0-x^3+color(white)(...)0-color(white)(...)x-color(white)(..)22+ A`

Where `A= 17/(x-2)xx(x-2) = 17`

`x^5-x^3-x-22+17" "=" "color(magenta)(x^5-x^3-x-5)->` as required