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 $=(x-1)$

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

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