How do you divide #(-x^4+5x^3+3x^2-6x-2)/(x^2-4) #?

1 Answer
Tony B
Jun 14, 2016

#-x^2+5x-1 +(14x-6)/(x^2-4)#

Explanation:

Given:#" "(color(blue)(-x^4+5x^3+3x^2-6x-2))/(x^2-4)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#" "color(blue)(-x^4+5x^3+3x^2-6x-2)#
#color(magenta)(-x^2)(x^2-4) ->color(white)(.)ul(-x^4 +0x^3+4x^2)" "larr" Subtract"#
#" "0+5x^3-x^2color(white)(.)-6x-2#
#color(magenta)(+5x)(x^2-4)->" "color(white)(....)ul(5x^3+0x^2-20x)" "larr" Subtract"#
#" "0-x^2+14x-2#
#color(magenta)(-1)(x^2-4) ->" "color(white)(..)ul(-x^2+0x+4)larr" Subtract"#
#" "0+14x-6#

#color(magenta)(-x^2+5x-1 +(14x-6)/(x^2-4)#

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