How do you divide #(x^3+2x^2-2x-4) / (x^2+1)# using polynomial long division?

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Answer 1 · 2017-05-20T15:24:06

The quotient is #=(x+2)# and the remainder is #=(-3x-6)#

Let's perform the long division

#color(white)(aaaa)##x^2+1##color(white)(aaaa)##|##x^3+2x^2-2x-4##color(white)(aaaa)##|##x+2#

#color(white)(aaaaaaaaaaaaaaa)##x^3+00+x#

#color(white)(aaaaaaaaaaaaaaaa)##0+2x^2-3x-4#

#color(white)(aaaaaaaaaaaaaaaaaa)##+2x^2-00+2#

#color(white)(aaaaaaaaaaaaaaaaaaaa)##+0-3x-6#

Therefore,

#(x^3+2x^2-2x-4)/(x^2+1)=x+2+(-3x-6)/(x^2+1)#

The quotient is #=(x+2)# and the remainder is #=(-3x-6)#