How do you divide #(-6x^4-3x^3-2x^2-4x-7)/(x^2+3) #?

1 Answer
Leland Adriano Alejandro
Jul 28, 2016

#color(blue)((-6x^4-3x^3-2x^2-4x-7)/(x^2+3)=-6x^2-3x+16+(5x-55)/(x^2+3))#

Explanation:

#(-6x^4-3x^3-2x^2-4x-7)/(x^2+3)#

The Long Division method:

# " " " " " " " " " " " "underline(-6x^2-3x+16" " " " " " " " " " " " " " " " " " ")#
#x^2+0*x+3|~-6x^4-3x^3-2x^2-4x-7#
#" " " " " " " " " " " "underline(-6x^4+0*x^3-18x^2" " " " " ")#
#" " " " " " " " " " " " " " " " "-3x^3+16x^2-4x-7#
#" " " " " " " " " " " " " " " " "underline(-3x^3+0*x^2-9x)#
#" " " " " " " " " " " " " " " " " " " " " "16x^2+5x-7#
#" " " " " " " " " " " " " " " " " " " " " "underline(16x^2+0*x+48)#
#" " " " " " " " " " " " " " " " " " " " " " " " " "+5x-55 larr#Remainder

The answer

#color(blue)((-6x^4-3x^3-2x^2-4x-7)/(x^2+3)=-6x^2-3x+16+(5x-55)/(x^2+3))#

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