# How do you factor 6x^3 + 29x^2 + 23x - 30 = 0?

Oct 3, 2015

Technically, you factor $6 {x}^{3} + 29 {x}^{2} + 23 x - 30$ to solve $6 {x}^{3} + 29 {x}^{2} + 23 x - 30 = 0$

Step 1: find a linear factor
Step 2: factorise and factorise

#### Explanation:

$6 {x}^{3} + 29 {x}^{2} + 23 x - 30 = 0$

By inspection
$6 {\left(- 3\right)}^{3} + 29 {\left(- 3\right)}^{2} + 23 \left(- 3\right) - 30$
$= - 162 + 261 - 69 - 30 = 0$

Thus $\left(x + 3\right)$ is a factor

By inspection
$\left(x + 3\right) \left(6 {x}^{2} + 11 x - 10\right) = 0$
$\left(x + 3\right) \left(3 x - 2\right) \left(2 x + 5\right) = 0$
$x = - 3$ or$x = \frac{2}{3}$ or $x = - \frac{5}{2}$