How do you find the quotient of $(x^3+2x^2-7x-2)/(x-2)$ using long division?

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Answer 1 · 2017-02-02T11:11:53

The quotient is $=color(red)(x^2+4x+1)$

Let's do the long division

$color(white)(aaaa)$ $x^3+2x^2-7x-2$ $color(white)(aaaa)$ $|$ $color(blue)(x-2)$

$color(white)(aaaa)$ $x^3-2x^2$ $color(white)(aaaaaaaaaaaa)$ $|$ $color(red)(x^2+4x+1)$

$color(white)(aaaaa)$ $0+4x^2-7x$

$color(white)(aaaaaaa)$ $+4x^2-8x$

$color(white)(aaaaaaaaa)$ $+0+x-2$

$color(white)(aaaaaaaaaaaaa)$ $+x-2$

$color(white)(aaaaaaaaaaaaa)$ $+0-0$

The remainder is $=0$ and the quotient is $color(red)(x^2+4x+1)$

How do you find the quotient of (x^3+2x^2-7x-2)/(x-2)(x^3+2x^2-7x-2)/(x-2) using long division?