# How do you divide (x^3-3x-2) / (x+8)  using polynomial long division?

May 20, 2016

$\frac{{x}^{3} - 3 x - 2}{x + 8} \text{ " =" } {x}^{2} - 8 x + 61 - \frac{490}{x + 8}$

#### Explanation:

Using different variables but the approach is the same; have a look at:$\text{ }$ https://socratic.org/s/auC4VyMH

Solution without as much explanation as shown on the hyperlinked page.

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$\text{ } {x}^{2} - 8 x + 61$
x+8" "bar("| "x^3+0x^2-3x-2)
" "color(blue)(underline(x^3+8x^2 )" " larrx^2(x+8) " subtract")
" "color(brown)(0-8x^2-3x-2" " larr "Remainder")
" "color(blue)(underline(-8x^2-64x )" "larr -8x(x+8)" subtract")
" "color(brown)(0+61x-2" "larr" Remainder")
" "color(blue)(underline(61x+488)" "larr" "61(x+8)" subtract")
" "color(brown)(0-490" "larr" Remainder")

$\textcolor{b r o w n}{\text{remainder } \to - \frac{490}{x + 8}}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Putting it all together}}$

$\textcolor{b l u e}{\frac{{x}^{3} - 3 x - 2}{x + 8} \text{ " =" } {x}^{2} - 8 x + 61 - \frac{490}{x + 8}}$.....(1)

'@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
'@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
$\textcolor{m a \ge n t a}{\text{Check}}$
${x}^{2} - 8 x + 61 - \frac{490}{x + 8}$

underline(" "x+8)" "larr" multiply"
${x}^{3} - 8 x + 61 x + 0 - \frac{490 x}{x + 8} \text{ "larr" multiplied by } x$

underline(" "+8x^2-64x+488+0-3920/(x+8))" "larr" multiplied by 8"
$\textcolor{g r e e n}{{x}^{3} + 0 {x}^{2} - 3 x + 488 - \frac{490 x}{x + 8} - \frac{3920}{x + 8}}$...(2)

'........................................

Consider $- \frac{490 x}{x + 8} - \frac{3920}{x + 8}$

$\frac{- 490 \left(x - 8\right)}{x - 8} = - 490$
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So equation (2) becomes

color(green)(x^3+0x^2-3x+488-490#

$\textcolor{g r e e n}{{x}^{3} - 3 x - 2}$

$\textcolor{red}{\text{Solution is correct}}$