How do you divide (-x^4+6x^3+8x+12)/(x^2-5x+2)?

Jan 6, 2018

$- {x}^{2} + x + 7 + \frac{41 x - 2}{{x}^{2} - 5 x + 2}$

Explanation:

Using place keepers. For example: $0 {x}^{2}$

$\textcolor{w h i t e}{\text{ddddddddddddddddd}} - {x}^{4} + 6 {x}^{3} + 0 {x}^{2} + 8 x + 12$
 color(magenta)(-x^2)(x^2-5x+2)-> ul(-x^4+5x^3-2x^2 larr" Subtract"
$\textcolor{w h i t e}{\text{dddddddddddddddddddd")0+ color(white)("d}} {x}^{3} + 2 {x}^{2} + 8 x + 12$
$\textcolor{m a \ge n t a}{+ x} \left({x}^{2} - 5 x + 2\right) \to \textcolor{w h i t e}{\text{ddddd")ul(+color(white)("d")x^3-5x^2+2x larr" Subtract}}$
$\textcolor{w h i t e}{\text{ddddddddddddddddddddddd")0 color(white)("d")+ color(white)(".")7x^2 +color(white)("d}} 6 x + 12$
$\textcolor{m a \ge n t a}{+ 7} \left({x}^{2} - 5 x + 2\right) \to \textcolor{w h i t e}{\text{dd..dddddd")ul( +color(white)("d")7x^2-35x+14 larr" Sub.}}$
color(magenta)("Remainder "-> color(white)("ddddddddddddddddd") 0 color(white)("d")+41x-2)

$\textcolor{m a \ge n t a}{- {x}^{2} + x + 7 + \frac{41 x - 2}{{x}^{2} - 5 x + 2}}$