How do you divide (x^3-7x^2+17x+13 ) / (2x+1)  using polynomial long division?

Jan 22, 2017

(x^3-7x^2+17x+13)/(2x+1) = color(magenta)(1/2x^2-15/4x+83/8+(color(blue)(21/8))/(2x+1)

Explanation:

$\text{ } {x}^{3} - 7 {x}^{2} + 17 x + 13$
$\textcolor{m a \ge n t a}{\frac{1}{2} {x}^{2}} \left(2 x + 1\right) \to \text{ul(x^3+1/2x^2) larr" Subtract}$
$\text{ } 0 - \frac{15}{2} {x}^{2} + 17 x + 13$
$\textcolor{m a \ge n t a}{- \frac{15}{4} x} \left(2 x + 1\right) \to \text{ "color(white)()ul(-15/2x^2-15/4x ) larr" Subtract}$
$\text{ } 0 + \frac{83}{4} x + 13$
$\textcolor{m a \ge n t a}{\frac{83}{8}} \left(2 x + 1\right) \to \text{ "color(white)(xxxxxx)ul(83/4x+83/8 ) larr" Subtract}$
$\text{ "color(blue)(0 +21/8) larr" Remainder}$

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Hence, quotient is ${x}^{3} - 7 {x}^{2} + 17 x + 13$ and remainder is $\frac{21}{8}$ and

(x^3-7x^2+17x+13)/(2x+1) = color(magenta)(1/2x^2-15/4x+83/8+(color(blue)(21/8))/(2x+1)