# How do you find all zeros of the function F(x)=2x^3-14x^2-56x-40 given 10 as a zero?

Nov 2, 2016

The other two zeros are $- 1$ and $- 2$

#### Explanation:

Since we are told that $10$ is a zero, $\left(x - 10\right)$ must be a factor:

$F \left(x\right) = 2 {x}^{3} - 14 {x}^{2} - 56 x - 40$

$\textcolor{w h i t e}{F \left(x\right)} = \left(x - 10\right) \left(2 {x}^{2} + 6 x + 4\right)$

$\textcolor{w h i t e}{F \left(x\right)} = 2 \left(x - 10\right) \left({x}^{2} + 3 x + 2\right)$

$\textcolor{w h i t e}{F \left(x\right)} = 2 \left(x - 10\right) \left(x + 2\right) \left(x + 1\right)$

So the other two zeros are $x = - 2$ and $x = - 1$