# How do you solve 2x^3+x^2>6x using a sign chart?

Oct 18, 2016

the answer is $- 2 < x < 0$ and $x > \frac{3}{2}$

#### Explanation:

We need to factorise the expresson
$2 {x}^{3} + {x}^{2} - 6 x > 0 \implies x \left(2 {x}^{2} + x - 6\right) > 0$
$\implies$ $x \left(2 x - 3\right) \left(x + 2\right) > 0$
So the key points we have to look at are $x = 0$ $x = \frac{3}{2}$ and $x = - 2$

If $x < - 2$ the expression is$< 0$
If $- 2 < x < 0$ the expression is $> 0$
If $0 < x < \frac{3}{2}$ the expression is $< 0$
If $x > \frac{3}{2}$ the expression is $> 0$
So the answer is $- 2 < x < 0$ and $x > \frac{3}{2}$