How do you long divide #(x^3)/(x^2+2x+1)#?

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Answer 1 · 2018-07-11T13:58:51

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

Perform the long division

#color(white)(aaaa)##x^3+0x^2+0x+0##color(white)(aaaa)##|##x^2+2x+1#

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

#color(white)(aaaaa)##0-2x^2-x#

#color(white)(aaaaaaa)##-2x^2-4x-2#

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

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

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