How do you divide #(-2x^3+7x^2-4x-1)/(3x-1) #?

1 Answer
Tony B
Aug 9, 2018

#-2/3x^2+19/9x-17/27-44/(81x-27)#

Explanation:

#color(white)("ddddddd.ddddddd")-2x^3+7x^2-4x-1#
#color(magenta)(-2/3x^2)(3x-1) ->ul(-2x^3+2/3x^2 larr" Subtract")#
#color(white)("ddddddddddddddddd")0+19/3x^2-4x-1#

#color(magenta)(+19/9x)(3x-1)->color(white)("ddddd.")ul(19/3x^2-19/9xlarr" Subtract")#
#color(white)("dddddddddddddddddddddd")0color(white)("dd")-17/9x-1#

#color(magenta)(-17/27)(3x-1) ->color(white)("dddddddddddd")ul( -17/9x+17/27larr" Subtract")#
#color(magenta)("Remainder"-> color(white)("ddddddddddddddddd")0color(white)("d")-44/27)#

#color(magenta)(-2/3x^2+19/9x-17/27 -[44/27color(black)(-:(3x-1))])#

#-2/3x^2+19/9x-17/27-44/(81x-27)#

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