Question

How do you divide `( -3x^3+ 4x^2 + 12x + 9 )/(x - 2 )`?

Answer 1

`(-3x^3+4x^2+12x+9)/(x-2) " "=" "-3x^2-2x+8+25/(x-2)`

Explanation:

`" "-3x^3+4x^2+12x+9" ............checked"`
`color(red)(-3x^2)(x-2)-> ul(-3x^3+6x^2) larr" subtract .........corrected"`
`" "0-2x^2+12x+9`
`color(red)(-2x)(x-2)->" "ul(-2x^2+4x)larr" subtract"`
`" "0+8x+9`
`color(red)(+8)(x-2)->" "ul(8x-16)larr" subtract"`
`" "0color(red)(+25 larr" remainder")`

`(-3x^3+4x^2+12x+9)/(x-2) " "=" "color(red)(-3x^2-2x+8+)color(red)(25)/(x-2)`

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Checked in Maple: