Question

How do you divide `( x^3-4x^2-17x+60 )/(3-2x)`?

Answer 1

`-1/2x^2+5/4x+83/8 +231/(8(3-2x))" Corrected"`

Explanation:

`color(white)("-----------------------------")+x^3-4x^2-17x+60`
`color(magenta)(-1/2x^2)(3-2x)->color(white)("-----")ul(+x^3-3/2x^2 larr" Subtract ")`
`color(white)("--------------------------------")0color(white)("-")-5/2x^2-17x+60 color(red)(larr" Corrected"`
`color(magenta)(+5/4x)(3-2x)->color(white)("------------") ul(-5/2x^2+15/4x larr" Subtract")`
`color(white)("---------------------------------------")0 color(white)("----")-83/4x+60`

`color(magenta)(+83/8)(3-2x)->color(white)("----------------------")ul(-83/4x+249/8larr" Subt.")`
`color(magenta)("Remainder"->color(white)("--------------------------------") 0+231/8)`

Giving:

`color(magenta)( -1/2x^2+5/4x+83/8 +231/(8(3-2x)))`

Answer 2

`-1/2x^2+5/4x+83/8+(231)/(8(-2x+3))`

Explanation:

`(x^3-4x^2-17x+60)/(3-2x)`

`color(white)(..........)color(white)(...)-1/2x^2+5/4x+83/8`
`-2x+3|overline(x^3-4x^2-17x+60)`
`color(white)(................)ul(x^3-3/2x^2)`
`color(white)(......................)-5/2x^2-17x`
`color(white)(......................)ul(-5/2x^2+15/4x)`
`color(white)(.................................)-83/4x+60`
`color(white)(..................................)ul(-83/4x+249/8)`
`color(white)(................................................)231/8`

`(x^3-4x^2-17x+60)/(3-2x) = -1/2x^2+5/4x+83/8+(231)/(8(-2x+3))`