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

#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)))#

#(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))#