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 $=x-2$

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

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