# How do you use the factor theorem to determine whether y-2 is a factor of 3y^4 – 6y^3 – 5y + 10?

May 14, 2018

$\left(y - 2\right) \text{ is a factor}$

#### Explanation:

$\text{if "y-2" is a factor then } f \left(2\right) = 0$

$f \left(2\right) = 3 {\left(2\right)}^{4} - 6 {\left(2\right)}^{3} - 5 \left(2\right) + 10$

$\textcolor{w h i t e}{f \left(2\right)} = 48 - 48 - 10 + 10 = 0$

$\Rightarrow \left(y - 2\right) \text{ is a factor of the polynomial}$