Question

How do you simplify and divide `(b^3+8b^2-20b)div(b-2)`?

Answer 1

`b^3+8b^2-20bdivcolor(blue)(b^2+10b)`
`color(white)("XXXXXXXXXXXXX")`with a remainder of `color(red)0`

Explanation:

Using synthetic division:
`{: (,,color(gray)(b^3),color(gray)(b^2),color(gray)(b^1),color(gray)(b^0)), (," | ",1,+8,-20,color(white)("x")0), (+," | ",ul(" "),ul(color(white)("0")2),ul(color(white)("xx")20),ul(color(white)("x")0)), (xx 2," | ",1,10,color(white)("xx")0,color(white)("x")0), (,,color(gray)(b^2),color(gray)(b^1),color(white)("x")color(gray)(b^0),color(gray)("R")) :}`

Answer 2

`color(magenta)(b^2+10b`

Explanation:

`(b^3+8b^2-20b)-:(b-2)`

`color(white)(...)color(white)(.......)b^2+10b`
`b-2|overline(b^3+8b^2-20b)`
`color(white)(............)ul(b^3-2b^2)`
`color(white)(......................)10b^2-20b`
`color(white)(......................)ul(10b^2-20b)`

`color(magenta)(b^3+8b^2-20b-:b-2 = b^2+10b`