# What are the factors for 6w^3 + 30w^2 -18w - 90 = 0?

May 9, 2015

$6 {w}^{3} + 30 {w}^{2} - 18 w - 90 = 0$

Grouping
$\textcolor{red}{\left(6 {w}^{3} + 30 {w}^{2}\right)} - \textcolor{b l u e}{\left(18 w + 90\right)} = 0$

$\textcolor{red}{\left(6 {w}^{2}\right) \left(w + 5\right)} - \textcolor{b l u e}{\left(18\right) \left(w + 5\right)}$

$\left(6 {x}^{2} - 18\right) \left(w + 5\right)$

Final check for other obvious common factors:
$6 \left({x}^{2} - 3\right) \left(w + 5\right)$

$\left({x}^{2} - 3\right)$ could be factored as $\left(x + \sqrt{3}\right) \left(x - \sqrt{3}\right)$ but it is not obvious that this would be any clearer.