Question

Divide x^4 + 2x^2 + 1 by x+1 .​

Answer 1

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

Explanation:

`(x^4+2x^2+1)/(x+1)\\\mathrm{Divide}\:(x^4+2x^2+1)/(x+1):\quad (x^4+2x^2+1)/(x+1)=x^3+(-x^3+2x^2+1)/(x+1)\\=x^3+(-x^3+2x^2+1)/(x+1)\\\mathrm{Divide}\:(-x^3+2x^2+1)/(x+1):\quad (-x^3+2x^2+1)/(x+1)=-x^2+(3x^2+1)/(x+1)\\=x^3-x^2+(3x^2+1)/(x+1)\\\mathrm{Divide}\:(3x^2+1)/(x+1):\quad (3x^2+1)/(x+1)=3x+(-3x+1)/(x+1)\\=x^3-x^2+3x+(-3x+1)/(x+1)\\\mathrm{Divide}\:(-3x+1)/(x+1):\quad (-3x+1)/(x+1)=-3+(4)/(x+1)\\=x^3-x^2+3x-3+(4)/(x+1)`