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

1 Answer
Barney V.
Dec 13, 2017

#color(magenta)(-x^2-4x+1# plus remainder of #color(magenta)(20x-6#

Explanation:

#(-x^4-4x^3-3x^2+4x-2)/(x^2+4)#

#color(white)(..........)color(white)(.)color(magenta)(-x^2-4x+1#
#w-2|overline(-4x^4-4x^3-3x^2+4x-2)#
#color(white)(..............)ul(-x^4+0x-4x^2)#
#color(white)(.....................)-4x^3+x^2+4x#
#color(white)(......................)ul(-4x^3+0x-16x-2)#
#color(white)(..................................)x^2+20x-2#
#color(white)(..................................)ul(x^2+0x+4)#
#color(white)(..........................................)color(magenta)(20x-6#

#(-x^4-4x^3-3x^2+4x-2)/(x^2+4) = color(magenta)(-x^2-4x+1# plus remainder of #color(magenta)(20x-6#

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