# How do you divide ( x^5 - x^3 + x - 2 x - 5)/(x - 2 )?

May 4, 2016

Have a look at https://socratic.org/s/aubpbqz9. Not the same values but the process is the same. Unless I have gone wrong, your answer should be:
$\text{ Corrected solution} \to {x}^{4} + 2 {x}^{3} + 3 {x}^{2} + 6 x + 11 + \frac{17}{x - 2}$

#### Explanation:

Using place holders such as $0 {x}^{2}$ which is the same as $0$

$\text{ } {x}^{4} + 2 {x}^{3} + 3 {x}^{2} + 6 x + 11$
" "x-2bar(|" "color(magenta)(x^5+0x^4-x^3+0x^2-x-5))
$\textcolor{b r o w n}{{x}^{4} \left(x - 2\right) \to} \text{ "underline(x^5-2x^4)" " larr} S u b t r a c t$
$\text{ } 0 + 2 {x}^{4} - {x}^{3}$
$\textcolor{b r o w n}{2 {x}^{3} \left(x - 2\right)} \to \text{ } \underline{2 {x}^{4} - 4 {x}^{3}} \leftarrow S u b t r a c t$
$\text{ } 0 + 3 {x}^{3} + 0 {x}^{2}$
$\textcolor{b r o w n}{3 {x}^{2} \left(x - 2\right)} \to \text{ } \underline{3 {x}^{3} - 6 {x}^{2}} \leftarrow S u b t r a c t$
$\text{ } 0 + 6 {x}^{2} - x$
$\textcolor{b r o w n}{6 x \left(x - 2\right)} \to \text{ } \underline{6 {x}^{2} - 12 x}$
$\text{ } 0 + 11 x - 5$
$\textcolor{b r o w n}{11 \left(x - 2\right)} \to \text{ } \underline{11 x - 22}$
color(brown)(" Remainder") ->" "+17

${x}^{4} + 2 {x}^{3} + 3 {x}^{2} + 6 x + 11 + \frac{17}{x - 2}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Check}}$

$\text{ } {x}^{4} + 2 {x}^{3} + 3 {x}^{2} + 6 x + 11 + \frac{17}{x - 2}$

$\underline{\textcolor{w h i t e}{/ / / / / / / / / / / / / / / / / / \frac{/}{.}} x - 2} \text{ "larr "Multiply}$
${x}^{5} + 2 {x}^{4} + 3 {x}^{2} + 6 {x}^{2} + 11 x$
$\underline{0 {x}^{5} - 2 {x}^{4} - 4 {x}^{3} - 6 {x}^{2} - 12 x - 22 + A} \text{ "larr" Add}$
${x}^{5} + \text{ } 0 - {x}^{3} + \textcolor{w h i t e}{\ldots} 0 - \textcolor{w h i t e}{\ldots} x - \textcolor{w h i t e}{. .} 22 + A$

Where $A = \frac{17}{x - 2} \times \left(x - 2\right) = 17$

${x}^{5} - {x}^{3} - x - 22 + 17 \text{ "=" } \textcolor{m a \ge n t a}{{x}^{5} - {x}^{3} - x - 5} \to$ as required