Question

Question #c7b2b

Answer 1

The remainder is `=-3` and the quotient is `=3y^2-7`

Explanation:

You can perform a long division

`color(white)(aaaa)` `15y^3-27y^2-35y+60` `color(white)(aaaa)` `|` `5y-9`

`color(white)(aaaa)` `15y^3-27y^2` `color(white)(aaaaaaaaaaaaaa)` `|` `3y^2-7`

`color(white)(aaaaaaaa)` `0-0-35y+60`

`color(white)(aaaaaaaaaaaaa)` `-35y+63`

`color(white)(aaaaaaaaaaaaaaaaa)` `0-3`

The remainder is `=-3` and the quotient is `=3y^2-7`

You can check by doing a multiplication

`15y^3-27y^2-35y+60=(5y-9)(3y^2-7)-3`

Answer 2

`y^2+18/5y-13/25+1383/(125y-225)`

Same as:

`y^2+18/5y-13/25+1383/(25(5y-9))`

Explanation:

Given`" "(5y^3-27y^2-35y+60)-:(5y-9)`

`" "5y^3-27y^2-35y+60`
`color(magenta)(y^2)(5y-9)->" "ul(5y^3-9y^2) larr" Subtract"`
`" "0-18y^2-35y+60`
`color(magenta)(18/5y)(5y-9)->" "ul(color(white)(.)18y^2-162/5y) larr" Subtract"`
`" "0-color(white)(.)13/5y+60`
`color(magenta)(-13/25)(5y-9)->" "ul(-13/5y+117/25) larr" Subtract"`
`color(magenta)(" Remainder "->+1383/25)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(magenta)(y^2+18/5y-13/25+(1383/25 -:(5y-9)))`

`y^2+18/5y-13/25+1383/(125y-225)`