How do you divide $\frac{2 x^{3} + 2 x^{2} + 4 x + 4}{x^{2} + 8 x + 4}$ $(2x^3+2x^2+4x+4)/(x^2+8x+4)$ ?

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How do you divide $\frac{2 x^{3} + 2 x^{2} + 4 x + 4}{x^{2} + 8 x + 4}$ $(2x^3+2x^2+4x+4)/(x^2+8x+4)$ ?

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Answer 1 · 2018-08-08T11:49:22

$\frac{2 x^{3} + 2 x^{2} + 4 x + 4}{x^{2} + 8 x + 4} = (2 x - 14) + \frac{108 x + 60}{x^{2} + 8 x + 4}$ $(color(blue)(2x^3+2x^2+4x+4))/color(red)(x^2+8x+4)=color(green)((2x-14))+(108x+60)/color(red)(x^2+8x+4)$

Explanation:

Here ,

Dividend $: 2 x^{3} + 2 x^{2} + 4 x + 4 and$ $:color(blue)(2x^3+2x^2+4x+4) and$

divisor $: x^{2} + 8 x + 4$ $: color(red)(x^2+8x+4)$

So ,

$color(white)(..................................)color(green)(ul(2x-14color(white)(.........))larrquotient$
$color(white)(..........)color(red)((x^2+8x+4))$ $|color(blue)(2x^3+2x^2+4x+4)$

$color(white)()color(violet)((color(red)(x^2+8x+4))*2xtocolor(white)()ul(2x^3+16x^2+8x)$ $color(white)(.......)lArr"subtract"$
$color(white)(.....................................)-14x^2-4x+4$

$color(white)()color(violet)((color(red)(x^2+8x+4))(-14)tocolor(white)()ul(-14x^2-112x-56)$ $color(white)(.......)lArr"subtract"$
$color(white)(..........................................)color(green)($ $color(white)(.........)108x+60larr"Remainder"$

Hence ,

$(color(blue)(2x^3+2x^2+4x+4))$ = $(color(red)(x^2+8x+4))(2x-14)+(108x+60)$

$Quotient :q(x)=color(green)(2x-14$ $"and Remainder " :r(x)=108x+60$

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How do you divide $\frac{2 x^{3} + 2 x^{2} + 4 x + 4}{x^{2} + 8 x + 4}$ $(2x^3+2x^2+4x+4)/(x^2+8x+4)$ ?

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How do you divide (2x^3+2x^2+4x+4)/(x^2+8x+4)2x3+2x2+4x+4x2+8x+4(2x^3+2x^2+4x+4)/(x^2+8x+4)?

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How do you divide $\frac{2 x^{3} + 2 x^{2} + 4 x + 4}{x^{2} + 8 x + 4}$ $(2x^3+2x^2+4x+4)/(x^2+8x+4)$ ?