How do you divide $\frac{- x^{4} - 4 x^{3} - 3 x^{2} + 4 x - 2}{x^{2} + 4}$ $(-x^4-4x^3-3x^2+4x-2)/(x^2+4)$ ?

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How do you divide $\frac{- x^{4} - 4 x^{3} - 3 x^{2} + 4 x - 2}{x^{2} + 4}$ $(-x^4-4x^3-3x^2+4x-2)/(x^2+4)$ ?

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Answer 1 · 2017-12-13T15:47:12

$- x^{2} - 4 x + 1$ $color(magenta)(-x^2-4x+1$ plus remainder of $20 x - 6$ $color(magenta)(20x-6$

Explanation:

$\frac{- x^{4} - 4 x^{3} - 3 x^{2} + 4 x - 2}{x^{2} + 4}$ $(-x^4-4x^3-3x^2+4x-2)/(x^2+4)$

$color(white)(..........)color(white)(.)color(magenta)(-x^2-4x+1$
$w-2|overline(-4x^4-4x^3-3x^2+4x-2)$
$color(white)(..............)ul(-x^4+0x-4x^2)$
$color(white)(.....................)-4x^3+x^2+4x$
$color(white)(......................)ul(-4x^3+0x-16x-2)$
$color(white)(..................................)x^2+20x-2$
$color(white)(..................................)ul(x^2+0x+4)$
$color(white)(..........................................)color(magenta)(20x-6$

$(-x^4-4x^3-3x^2+4x-2)/(x^2+4) = color(magenta)(-x^2-4x+1$ plus remainder of $color(magenta)(20x-6$

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How do you divide $\frac{- x^{4} - 4 x^{3} - 3 x^{2} + 4 x - 2}{x^{2} + 4}$ $(-x^4-4x^3-3x^2+4x-2)/(x^2+4)$ ?

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Explanation:

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How do you divide $\frac{- x^{4} - 4 x^{3} - 3 x^{2} + 4 x - 2}{x^{2} + 4}$ $(-x^4-4x^3-3x^2+4x-2)/(x^2+4)$ ?