How do you long divide #(x^4 - 2x^2 + 4x + 1) ÷ (x^3-x^2-x+1)#?

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Answer 1 · 2018-07-25T13:46:30

The remainder is #=4x# and the quotient is #=x+1#

Perform a long division

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

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

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

#color(white)(aaaaaaa)##+1x^3-1x^2-x+1#

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

The remainder is #=4x# and the quotient is #=x+1#

#(x^4+0x^3-2x^2+4x+1)/(x^3-x^2-x+1)=x+1+(4x)/(x^3-x^2-x+1)#