# How do you factor and find the zeroes of the polynomial y=-2x^4+10x^3-12x^2?

Feb 8, 2017

Zeroes at $x = 3 , x = 2 \mathmr{and} x = 0$.

#### Explanation:

Factor out an $- 2 {x}^{2}$:

$y = - 2 {x}^{2} \left({x}^{2} - 5 x + 6\right)$

$y = - 2 {x}^{2} \left(x - 3\right) \left(x - 2\right)$

Set to $0$ and solve for $x$:

$0 = - 2 {x}^{2} \left(x - 3\right) \left(x - 2\right)$

$x = 0 , 3 \mathmr{and} 2$

This has zeroes at $x = 3 , x = 2 \mathmr{and} x = 0$.

Hopefully this helps!