# How do you find the quotient of (x^3+6x^2-x-30) divided by (x^2+8x+15)?

Jun 6, 2018

Quotient is $x - 2$

#### Explanation:

${x}^{3} + 6 {x}^{2} - x - 30$

=${x}^{3} + 8 {x}^{2} + 15 x - 2 {x}^{2} - 16 x - 30$

=$x \cdot \left({x}^{2} + 8 x + 15\right) - 2 \cdot \left({x}^{2} + 8 x + 15\right)$

=$\left({x}^{2} + 8 x + 15\right) \cdot \left(x - 2\right)$

Hence quotient is $x - 2$

Jun 6, 2018

$\left({x}^{3} - 6 {x}^{2} - x - 30\right) \div \left({x}^{2} + 8 x + 15\right) = \textcolor{b l u e}{x - 2}$

#### Explanation:

It is possible to solve this by factoring but factoring cubic equations can be time consuming.
As an alternative, I would suggest using simple polynomial long division.

color(white)("XXXXXXXXX")ul(color(white)("xx")xcolor(white)("x")-2color(white)("xxxxxxxxxxxxx"))
x^2+8x+15" ) "x^3color(white)("x")+6x^2color(white)("x")-xcolor(white)("x")-30
color(white)("XXXXXXXXXx")ul(x^3color(white)("x")+8x^2+15x)
$\textcolor{w h i t e}{\text{XXXXXXXXXxxxx")-2x^x-16xcolor(white)("x}} - 30$
color(white)("XXXXXXXXXxxxx")ul(-2x^x-16xcolor(white)("x")-30)