Question

For the problem (a³-9a+2)/a-3, how should the remainder of 2 be written?

`(a^3-9a+2)/(a-3)`

Answer 1

`2/(a-3)`

Explanation:

`color(blue)("Checking that the remainder is 2")`

Using place keepers that have no value. Example `0a^2`

Write as `->color(white)("dd")a^3+0a^2-9a+2`
`color(magenta)(a^2)(a-3) ->color(white)("d")ul( a^3-3a^2 larr" Subtract")`
`color(white)("dddddddddddd")0+3a^2-9a+2`
`color(magenta)(3a)(a-3)->color(white)("ddddd")ul( 3a^2-9alarr" Subtract")`
`color(white)("dddddddddddddddd")0color(white)("d")+0color(magenta)(+2 larr" Remainder")`

The remainder of 2 has to split up into `(a-3)` parts so we have:

`(a^3-9a+2) -:(a-3) = color(magenta)(a^2+3a+2/(a-3)`