What is #(x^4 + 3x^3-x+2)/(x^2+2x+1)#?

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Answer 1 · 2017-08-01T13:24:50

The quotient is #=x^2+x-3# and the remainder is #=4x+5#

Let's perform a long division

#color(white)(aaaa)##x^2+2x+1##|##color(white)(aa)##x^4+3x^3+0x^2-x+2##|##color(white)(aa)##x^2+x-3#

#color(white)(aaaaaaaaaaaaaaaaaa)##x^4+2x^3+x^2#

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

#color(white)(aaaaaaaaaaaaaaaaaaaaa)##+x^3+2x^2+x#

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

#color(white)(aaaaaaaaaaaaaaaaaaaaaaaaaa)##-3x^2-6x-3#

#color(white)(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa)##0+4x+5#

The quotient is #=x^2+x-3# and the remainder is #=4x+5#

#(x^4+3x^3-x+2)/(x^2+2x+1)=(x^2+x-3)+(4x+5)/(x^2+2x+1)#