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

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Answer 1 · 2018-07-15T06:05:07

The remainder is #=(-2x-2)# and the quotient is #=(x-1)#

Perform a long division

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

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

#color(white)(aaaaa)##0-1x^2-1x-3#

#color(white)(aaaaaaa)##-1x^2+1x-1#

#color(white)(aaaaaaaaa)##-0-2x-2#

The remainder is #=(-2x-2)# and the quotient is #=(x-1)#

#(x^3-2x^2+0x-3)/(x^2-x+1)=(x-1)-(2x+2)/(x^2-x+1)#