Question #5f17d

1 Answer
Barney V.
Nov 5, 2017

#color(magenta)((x^4-81) / (x+3) = x^3-3x^2+3x-9# and remainder of #color(magenta)((-54)/(x+3)#

Explanation:

#color(white)(..........) color(white)(....)x^3-3x^2+3x-9#
#x+3|overline(x^4+0+0+0-81)#
#color(white)(............)ul(x^4+3x^3)#
#color(white)(................)-3x^3+0#
#color(white)(.................)ul(-3x^3-3x^2)#
#color(white)(...........................)+3x^2+0#
#color(white)(...........................)ul(+3x^2+9x)#
#color(white)(..................................)-9x-81#
#color(white)(....................................)ul(-9x-27)#
#color(white)(...........................................)-54#

#color(magenta)((x^4-81) / (x+3) = x^3-3x^2+3x-9# and remainder of #color(magenta)((-54)/(x+3)#

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