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

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

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Answer 1 · 2017-02-02T11:11:53

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

Explanation:

Let's do the long division

$a a a a$ $color(white)(aaaa)$ $x^{3} + 2 x^{2} - 7 x - 2$ $x^3+2x^2-7x-2$ $a a a a$ $color(white)(aaaa)$ $∣$ $|$ $x - 2$ $color(blue)(x-2)$

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

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

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

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

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

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

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

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

1 Answer

Explanation:

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How do you find the quotient of (x^3+2x^2-7x-2)/(x-2)x3+2x2−7x−2x−2(x^3+2x^2-7x-2)/(x-2) using long division?

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Explanation:

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