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

2 Answers
Feb 3, 2018

-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)))

Feb 3, 2018

-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))