# How do you find the quotient of (6x^3+5x^2+9)div(2x+3) using long division?

Mar 15, 2017

Quotient: $3 {x}^{2} - 2 x + 3$
(see below for derivation using long division)

#### Explanation:

color(white)("XXXxX")underline(color(white)("x")3x^2color(white)("x")-2xcolor(white)("xx")+3color(white)("XXXX"))
$2 x + 3 \textcolor{w h i t e}{\text{x"))color(white)("x")6x^3color(white)("x")+5x^2color(white)("x")+0xcolor(white)("x}} + 9$
color(white)("XXXXXX")ul(6x^3color(white)("x")+9x^2)
$\textcolor{w h i t e}{\text{XXXXXXXXX")-4x^2color(white)("x}} + 0 x$
color(white)("XXXXXXXXX")ul(-4x^2color(white)("x")-6x)
$\textcolor{w h i t e}{\text{XXXXXXXXXXXXXXX")6xcolor(white)("x}} + 9$
color(white)("XXXXXXXXXXXXXXX")ul(6xcolor(white)("x")+9)
$\textcolor{w h i t e}{\text{XXXXXXXXXXXXXXXXXXX}} 0$