How do you divide (2x^3 + x^2 – 3x – 40)/(3x + 1)?

Oct 1, 2017

$\frac{2}{3} {x}^{2} + \frac{1}{9} x - \frac{28}{27} + \frac{1052}{26 \left(3 x + 1\right)}$

Explanation:

$\textcolor{w h i t e}{\text{ddddddddddddddd}} 2 {x}^{3} + {x}^{2} - 3 x - 40$
color(magenta)(2/3x^2)(3x+1)color(white)("d")->color(white)("d")ul(2x^3+2/3x^2larr" Subtract"
$\textcolor{w h i t e}{\text{ddddddddddddddddd}} 0 + \frac{1}{3} {x}^{2} - 3 x - 40$
$\textcolor{m a \ge n t a}{\frac{1}{9} x} \left(3 x + 1\right) \textcolor{w h i t e}{\text{dd")->color(white)("dddddd") ul(1/3x^2+1/9x larr" Subtract}}$
$\textcolor{w h i t e}{\text{dddddddddddddddddddddd}} 0 - \frac{28}{9} x - 40$
$\textcolor{m a \ge n t a}{- \frac{28}{27}} \left(3 x + 1\right) \textcolor{w h i t e}{\text{d")-> color(white)("ddddddddd")ul(-28/9x-28/27larr" Subtract}}$
$\textcolor{w h i t e}{\text{ddddddddddd")" Remainder "->color(white)("d")0color(white)("dd}} + \frac{1052}{27}$

Converting the remainder into part of the division $\frac{1052}{27} \div \left(3 x + 1\right)$

$\textcolor{m a \ge n t a}{\frac{2}{3} {x}^{2} + \frac{1}{9} x - \frac{28}{27} + \frac{1052}{26 \left(3 x + 1\right)}}$