Question

How do you divide `( -3x^3+ 3x^2-30x-72 )/(x + 1 )`?

Answer 1

The fastest method is probably synthetic division; giving:
`(-3x^2+6x-36) -36/(x+1)`

Explanation:

`(color(blue)(-3)x^3,color(blue)(+3)x^2,color(blue)(-30)x,color(blue)(-72)) div (xcolor(red)(+)color(green)(1))`

`{: (,,color(blue)(-3),color(blue)(+3),color(blue)(-30),color(blue)(-72)), (,,,+3,-6,+36), (xx (color(red)(-)color(green)(1)),"|",bar(color(cyan)(-3)),bar(color(cyan)(+6)),bar(color(cyan)(-36)),bar(color(brown)(-36))) :}`

`color(cyan)(-3)x^2color(cyan)(+6)xcolor(cyan)(-36)` with a remainder of `(color(brown)(-36))`