Question

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

Answer 1

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

Explanation:

Note that I use place keepers that have no value. This is done to make sure things line up properly. Example`-> 0x^2`

Numerator`" "->" "x^4+0x^3+0x^2-3x-5`
`color(magenta)(x^3)(x+2)" "->" "ul(x^4+2x^3)" "larr" Subtract"`
`" "0-2x^3+0x^2-3x-5`
`color(magenta)(-2x^2)(x+2)" "->" "ul( -2x^3-4x^2)" "larr" Subtract"`
`" "0+4x^2-3x-5`
`" "color(magenta)(4x)(x+2) " "->" "ul(4x^2+8x)" "larr" Subtract"`
`" "0-11x-5`
`color(magenta)(-11)(x+2)" "->" "ul(-11x-22 )" "larr" Sub."`
`" "0+17`

Where the final value of `color(magenta)("17 is the remainder")`

`(x^4-3x-5)/(x+2) = color(magenta)(x^3-2x^2+4x-11+17/(x+2))`